Thermodynamics_16 Marks.... 2nd Question

Question 2:

0.2m³ of air at 4 bar and 130^oC is contained in a system. A reversible adiabatic expansion takes place till the pressure falls to 1.02bar. The gas is then heated at constant pressure till enthalpy increases by 72.5KJ. Calculate work done and index of expansion if the above process is Polytrophic. Take C_p=1KJ/KgK     C _v=0.714KJ/Kg K..

Thermodyanamics_Important 2 Marks

1. Differentiate between open & closed system?

2.  Define zeroth law of thermodynamics ?

Zeroth law of thermodynamics states that when two systems are separately in thermal equilibrium with a third system, then they themselves are in thermal equilibrium with each other

3. Define quasi static process?

 The process is said to be quasi – static, it should proceed infinitesimally slow and follows continuous series of equilibrium states. Therefore, the quasi static, it should proceed infinitesimally slow and follows continuous series of equilibrium states. Therefore, the quasi static process may be an reversible process.

4. Define first law of thermodynamics?

First of thermodynamics states that when system undergoes a cyclic process the net heat transfer is equal to work transfer.

5. Define thermal Energy reservoir?

A thermal reservoir, a short-form of thermal energy reservoir, orthermal bath is a thermodynamic system with a heat capacity that is large enough that when it is in thermal contact with another system of interest or its environment, its temperature remains effectively constant.

6.Write down differences between refrigerator & heat pump?

Heat pump is a device which operating in cyclic process, maintains the temperature of a hot body at a temperature higher than the temperature of surroundings. A refrigerator is a device which operating in a cyclic process, maintains the temperature of a cold body at a temperature lower than the temperature of the surroundings.

7. Define Daltons law of  Partial Pressure?

The pressure of a mixture of gases is equal to the sum of the partial pressures exerted by individual gases if each one of them occupied separately in the total volume of the mixture at mixture temperature. p = p1 +p2+p3+….pk

8. Define latent heat of evaporation.

The amount of heat added during heating of water boiling point to dry saturated stage is called as latent heat of vaporization or enthalpy of vaporization or latent heat of steam.

9.Define dryness fraction of steam. (or) What is quality of steam?

It is defined as the ratio of the mass of the total steam actually present to the mass of the total steam.

Dryness fraction


10. Explain Joule Thompson effect?

a change in temperature of a thermally insulated gas when it is forced through a small hole or a porous material. For each gas there is a temperature of inversion above which the change is positive and below which it is negative. Also called: Joule-Kelvin effect.

11. Differentiate Control volume and Control mass?

The control mass system may be defined as a system having some mass and surrounded by a fixed boundary i.e. transfer of mass is not allowed but energy transfer may takes place. 

In case of control volume system energy and mass both can interact with system and surrounding. When mass of a system is fixed then there is only one difference between these two type of system i.e. identity.

12.Draw the Pv and Ts diagram of Carnot cycle with process?

13. Define Entropy and Entropy Principle?

Entropy is an index of unavailability or degradation of energy.

Entropy Principle:
Form the Clausius inequality, ∫ δQ / T ≤ 0
As the entropy is a property of the system, therefore the cyclic integral of a property is zero and the above equation can also be written as:
∫ δQ / T ≤ ∫ dS
SQ / T ≤ dS
dS ≥ δQ / T
for isolated system, SQ = 0

therefore
(dS)_iso ≥ 0
For a reversible process: (dS) _iso = 0
Or
S = constant
For an irreversible process: dS) _iso > 0 or entropy increases.

Thus it may be concluded that entropy of an isolated system can never decrease. It always increases with every irreversible process and remains constant when the process is reversible. This is known as principle of entropy increase or in other words the entropy of principle.

14. Define Carnot's theorem and its Corollaries?

Carnot's theorem is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

This maximum efficiency  is defined to be:

where

 is the work done by the system (energy exiting the system as work),

 is the heat put into the system (heat energy entering the system),

 is the absolute temperature of the cold reservoir, and

 is the absolute temperature of the hot reservoir.

A corollary to Carnot's theorem states that: All reversible engines operating between the same heat reservoirs are equally efficient.

16. Methods to find the dryness fraction of the steam mixture?

17. Define super heated and sub cooled liquid?


sub cooling is the condition of liquid refrigerant in colder than minimum temperature ( saturation temperature) required to keep it from boiling and hence change from liquid to a gas state while

Super heat is the temperature of vapor above the boiling  point at particular pressure.

18. Define point function and path function?

The quantity which is independent on the process or path followed by the system is known as point functions. 

Example: Pressure, volume, temperature, etc., 

The quantities which are dependent on the process or path followed by the system are known as path functions. 

Example: Heat transfer, work transfer. 

19. Define Extensive and Intensive property?

The properties which are independent on the mass of the system is called intensive properties.

E.g., Pressure, Temperature, Specific Volume etc., 

The properties which are dependent on the mass of the system is called extensive properties.


E.g., Total energy, Total volume, weight etc.

Errors in Measurement System....

An error may be defined as the difference between the measured value and the actual value. For example, if the two operators use the same device or instrument for finding the errors in measurement, it is not necessary that they may get the similar results. There may be a difference between both measurements. The difference that occurs between both the measurements is referred to as an ERROR.

Sequentially, to understand the concept of errors in measurement, you should know the two terms that define the error. They are true value and measured value. The true value is impossible to find out the truth of quantity by experimental means. It may be defined as the average value of an infinite number of measured values. Measured value can be defined as the estimated value of true value that can be found by taking several measured values during an experiment.

Types of Errors in Measurement System

Generally errors are classified into three types: systematic errors, random errors and blunders.

1) Gross Errors
2) Blunders
3) Measurement Errors

Systematic Errors

• Instrumental Errors
• Environmental Errors
• Observational Errors 
• Theoretical Errors

Random Errors

Types of Errors in Measurement System

1) Gross Errors

Gross errors are caused by mistake in using instruments or meters, calculating measurement and recording data results. The best example of these errors is a person or operator reading pressure gage 1.01N/m2 as 1.10N/m2. It may be due to the person’s bad habit of not properly remembering data at the time of taking down reading, writing and calculating, and then presenting the wrong data at a later time. This may be the reason for gross errors in the reported data, and such errors may end up in calculation of the final results, thus deviating results.

2) Blunders

Blunders are final source of errors and these errors are caused by faulty recording or due to a wrong value while recording a measurement, or misreading a scale or forgetting a digit while reading a scale. These blunders should stick out like sore thumbs if one person checks the work of another person. It should not be comprised in the analysis of data.

3) Measurement Error

The measurement error is the result of the variation of a measurement of the true value. Usually, Measurement error consists of a random error and systematic error. The best example of the measurement error is, if electronic scales are loaded with 1kg standard weight and the reading is 10002grams, then

The measurement error is = (1002grams-1000grams) =2grams

Measurement Errors are classified into two types: systematic error and random errors

Systematic Errors

The Systematic errors that occur due to fault in the measuring device are known as systematic errors. Usually they are called as Zero Error – a positive or negative error. These errors can be detached by correcting the measurement device. These errors may be classified into different categories.

Systematic Errors

In order to understand the concept of systematic errors, let us classify the errors as:

• Instrumental Errors
• Environmental Errors
• Observational Errors
• Theoritical

Instrumental Errors

Instrumental errors occur due to wrong construction of the measuring instruments. These errors may occur due to hysteresis or friction. These types of errors include loading effect and misuse of the instruments. In order to reduce the gross errors in measurement, different correction factors must be applied and in the extreme condition instrument must be recalibrated carefully.

Environmental Errors

The environmental errors occur due to some external conditions of the instrument. External conditions mainly include pressure, temperature, humidity or due to magnetic fields. In order to reduce the environmental errors

• Try to maintain the humidity and temperature constant in the laboratory by making some arrangements.
• Ensure that there shall not be any external electrostatic or magnetic field around the instrument.

Observational Errors

As the name suggests, these types of errors occurs due to wrong observations or reading in the instruments particularly in case of energy meter reading. The wrong observations may be due to PARALLAX. In order to reduce the PARALLAX error highly accurate meters are needed: meters provided with mirror scales.

Theoretical Errors

Theoretical errors are caused by simplification of the model system. For example, a theory states that the temperature of the system surrounding will not change the readings taken when it actually does, then this factor will begin a source of error in measurement.

Random Errors

Random errors are caused by the sudden change in experimental conditions and noise and tiredness in the working persons. These errors are either positive or negative. An example of the random errors is during changes in humidity, unexpected change in temperature and fluctuation in voltage. These errors may be reduced by taking the average of a large number of readings.

Random Errors

Measurement Error Calculation

There are several ways to make a reasonable measurement error calculation such as estimating random errors and estimating systematic errors.

Estimating Random Errors

There are a number of ways to make a reasonable estimate of the random error in a particular measurement. The best way is to make a series of measurements of a given quantity (say, x) and calculate the mean and standard deviation (x ̅  & σ_x ) from this data.

The mean x ̅   is defined as

Where, Xi is the result of the i th measurements

‘N’ is the number of measurements

The standard variation is given by

If a measurement is repeated many times, then 68% of the measured valves will drop in the range  x ̅ ± σ_x

We become more positive that , is an accurate representation of the true value of the quantity x ̅ . The standard deviation of the mean σ_x is defined as

σ_(x ̅  )=σ_x⁄√N

The quantity σ_x is a good estimate of our uncertainty in  x ̅.  Notice that the measurement precision increases in proportion to √N  as we increase the number of measurements. The following example will clarify these ideas. Assume you made the following five measurements of a length:

Error Calculations

Therefore, the result is 22.84±.08mm

In some cases, it is hardly useful to repeat a measurement many times. In that situation, you can estimate frequently the error by taking account of the smallest division of the measuring instrument.

For example, when using a meter stick, one can measure, perhaps a half or sometimes even a fifth of a millimeter. So, the absolute error would be estimated to be around 0.5 mm or 0.2 mm.

STATIC & DYNAMIC CHARACTERISTICS OF MEASUREMENT SYSTEM

The performance characteristics of an instrument are mainly divided into two categories:

i) Static characteristics

ii) Dynamic characteristics

Static characteristics:

The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, i.e., do not vary with time, is called ‘static characteristics’.

The various static characteristics are:

i) Accuracy

ii) Precision

iii) Sensitivity

iv) Linearity

v) Reproducibility

vi) Repeatability

vii) Resolution

viii) Threshold

ix) Drift

x) Stability

xi) Tolerance

xii) Range or span

Accuracy:

It is the degree of closeness with which the reading approaches the true value of the quantity to be measured. The accuracy can be expressed in following ways:

a) Point accuracy:

Such accuracy is specified at only one particular point of scale.
It does not give any information about the accuracy at any other Point on the scale.

b) Accuracy as percentage of scale span:

When an instrument as uniform scale, its accuracy may be expressed in terms of scale range.

c) Accuracy as percentage of true value:

The best way to conceive the idea of accuracy is to specify it in
terms of the true value of the quantity being measured. Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. The precision is composed of two characteristics:

a) Conformity:

Consider a resistor having true value as 2385692 , which is being measured by an ohmmeter. But the reader can read consistently, a value as 2.4 M due to the nonavailability of proper scale. The error created due to the limitation of the scale reading is a precision error.

b) Number of significant figures:

The precision of the measurement is obtained from the number of significant figures, in which the reading is expressed. The significant figures convey the actual information about the magnitude & the measurement  precision of the quantity. The precision can be mathematically expressed as:

Where, P = precision
Xn = Value of nth measurement
Xn = Average value the set of measurement values

Sensitivity:

The sensitivity denotes the smallest change in the measured variable to which the instrument responds. It is defined as the ratio of the changes in the output of an instrument to a change in the value of the quantity to be measured. Mathematically it is expressed as,

Thus, if the calibration curve is liner, as shown, the sensitivity of the instrument is the slope of the calibration curve. If the calibration curve is not linear as shown, then the sensitivity varies with the input. Inverse sensitivity or deflection factor is defined as the reciprocal of sensitivity. Inverse sensitivity or deflection factor = 1/ sensitivity

Reproducibility:

It is the degree of closeness with which a given value may be repeatedly measured. It is specified in terms of scale readings over a given period of time.

Repeatability:

It is defined as the variation of scale reading & random in nature Drift:
Drift may be classified into three categories:

a) zero drift:

If the whole calibration gradually shifts due to slippage, permanent set, or due to undue warming up of electronic tube circuits, zero drift sets in.

b) span drift or sensitivity drift

If there is proportional change in the indication all along the upward scale, the drifts is called span drift or sensitivity drift.

c) Zonal drift:

In case the drift occurs only a portion of span of an instrument, it is called zonal drift.

Resolution:

If the input is slowly increased from some arbitrary input value, it will again be found that output does not change at all until a certain increment is exceeded. This increment is called resolution.

Threshold:

If the instrument input is increased very gradually from zero there will be some minimum value below which no output change can be detected. This minimum value defines the threshold of the instrument.

Stability:

It is the ability of an instrument to retain its performance throughout is
specified operating life.

Tolerance:

The maximum allowable error in the measurement is specified in terms of some value which is called tolerance.

Range or span:

The minimum & maximum values of a quantity for which an instrument is designed to measure is called its range or span.

Dynamic characteristics:

The set of criteria defined for the instruments, which are changes rapidly with time, is called ‘dynamic characteristics’.
The various static characteristics are:
i) Speed of response
ii) Measuring lag
iii) Fidelity
iv) Dynamic error

Speed of response:

It is defined as the rapidity with which a measurement system responds to changes in the measured quantity.

Measuring lag:

It is the retardation or delay in the response of a measurement system to changes in the measured quantity. The measuring lags are of two types:

a) Retardation type:

In this case the response of the measurement system begins immediately after the change in measured quantity has occurred.

b) Time delay lag:

In this case the response of the measurement system begins after a dead time after the application of the input. Fidelity: It is defined as the degree to which a measurement system indicates changes in the measurand quantity without dynamic error.

Dynamic error:

It is the difference between the true value of the quantity changing with time & the value indicated by the measurement system if no static error is assumed. It is also called measurement error.

A Cute Love story - Episode 8...!!!

I said, "Nethra, please don't talk non sense. Adithi and Mithra are the same to me. I trust God. You'll come back. You're the only one in my life"

She said, "A woman would love to hear this from her husband. I would be happy if I survive. Arjun, I love you, I wanna live with you in your love for infinite years. When I wanted to die I was saved and now when I wanna live I'm gonna die. I had repugnance towards life until you came into my life. I never thought love can be so good. You taught me what love is, what happiness is and what life is. You changed my seasons; you gave me reasons to smile, to laugh, to love and to live.

Now I like this life and I don't want to die so early. I never got what I wanted. The life with you till now is what I have been longing and yearning for all the days of my life. Parents like your parents, a husband like you who holds me in the palms of his hand and protects me like an apple of his eyes, children like you and me. I don't wanna die but live Arjun, I want to live this life. I want to live with you"

Sobbing she continued, "Whatever it is, God bless you and thanks a lot for you gave me a life in heaven. Though I don't want to die, I will still be happy if ill fate takes me because I lived a life to my heart's content"

As she was saying this, mom entered and I said, "Mom, she is scared to death and I can't console her or give her confidence"

Mom took her hands in hers and said, "Nethra, I spoke to the doctors they said this hospital is equipped with the latest instruments and the best doctors in town. You don't have to be scared or worried. As desired I'm gonna see my grandchild soon. After few years you're gonna give me another grandchild and I'm gonna raise them up. Don't worry about anything. Put your trust in God" saying this she kissed her forehead and stroked her gently.

I know my mom's kiss pacifies her and she was calm and said to me, "Please be with me"

I said, "It is my duty and responsibility to be with you in times of trouble and pain. Don't worry I'll be with you"

A couple of nurses brought the stretchers and took her to the operation theatres. I was with her holding her hands till she became unconscious. I wanted to cry aloud, I needed somebody to console me saying "She'll be safe" I had never felt like this before. Though Mom, Adithi and Mithra were present, nobody had the guts or courage to talk to be me as I was so depressed and dejected.

Little later I heard the cry of my little one; few minutes passed and a nurse came out; she placed my little one in my hands and said "It's a girl" I was happy yet I was looking at her with lots of queries and expectation for news about Nethra but without saying anything she left the place.

I kissed my little angel and hugged her to my bosom and held her tightly. She shook her body and her little hand hit my chest. I felt like she was consoling me, I felt like she's saying "It's alright dad, everything's gonna be fine soon. Mom is gonna comeback alive" I felt a great consolation and it's an unrivalled solace too. There is no match for the consolation, comfort and confidence she gave me that moment.

No one can ever give it again.

I felt happy and I blindly trusted that Nethra will come back.

Sometime later the doctor patted my back and said she's safe and out of danger.

I went near her and I wept with joy, it was such an emotion that I can't express in words but it can only be felt. The fear just vanished and I felt so... so good and happy. She woke up and smiling she asked, "Where is mom?" I kissed her forehead and said, it is a girl and mom is busy with her granddaughter. Wait I'll call her" saying this I ran to the veranda and called my mom. She came in along with Adithi and Mithra and gave my little angel to her and asked her to feed her.

Nethra took her, kissed her and fed her. Adithi and Mithra enquired about her health. My mom said, "I'm very happy to see both of you out of danger"

Nethra said, "Mom, you have to raise her up, wise, loving, patient, caring, affectionate, mischievous and naughty like Arjun. Teach her the rich heritage and cultural values of our country; specially the values of a family. Teach us parenting as well"

Mom said, "Sure and she left the room" with Adithi and Mithra.

She asked me to sit on the cot and she gave her to me. As I took my little one from Nethra, her hand got caught in Nethra's mangal sutra.

As Nethra was took out her hand she said, "Love gives meaning to everything even metals and stones"

I held her in one bosom and my little angel on the other and asked, "What does it mean to you?"

She said, "It means love and life. I love you. Arjun for this love you shower on me, my heart says you can do anything for this Man. I'm a slave to your love"

I kissed and said, "Love you too. You're not a slave but my queen" and looking at my little girl I said, "She is my little princess" As I said this, my little girl gave a small smile for a micro second with her tiny lips as if she was hearing to our conversation. I asked, so what shall we christen our angel?"

Nethra said, "POORNA"

Smiling I said, "My mother's name, lovely, but how will we address her"

She said, "Yeah, mom's name because POORNA means complete and fullness. Your mother and our daughter make our lives complete and let's fondly call her as Cuckoo or tweety"

I said, "Great, she'll be our little mom from now on"

Holding both of my angels on either of my bosom is one of the loveliest moments in my life.

A Cute Love story - Episode 7..!!!

She said, "Hold on I'm not yet done"

I said, "Bad girl, you don't know the rules of the game, you should hide before the counting ends"

I heard the sound of her anklets nearing me and her sweet perfume smell hit my nostrils. I felt her untying my hands as she was saying, "Is it, I'm sorry I don't know the rule"

She untied my hands and wrapped it around something, when I was trying to find it out what is in between my hands I felt something rolling my head. Before I could think of what was happening, I felt soft air brushing my ears and I heard her say "I LOVE YOU"

Next morning we woke up late, she was lying on my chest and her face was vivacious like a just blossomed rose. I stroked her head and said, "I loved the hide and seek game. Did you?" she murmured, "Hmmm, I liked it too"

I called my mom and after usual enquires I said, "Mom, the night dress was awesome; Thanks, nice selection" she gave a surprised look and grabbed the receiver from me and said, "mom, was it your selection? Hmmm anyway your idea was excellent and it worked out well, thanks a lot, we had a nice time" now I was shocked and grabbed the receiver from her and asked, "Mom, was the game your idea?" on the other end she said, "Turn on the speaker"

I turned it on and she continued, "I'm glad to know that both of you had a nice time. I just helped you people to start your family life as both of you were hesitating, scared and shy to take the initiative and from now on you can take it further. Relationships are fragile and need to be handled with care. Take this as a statement for life. Life is beautiful, enjoy it against the odds that come your way, be happy, make others happy and spread the happiness wherever you go. All the best, Have a happy honeymoon. Take care, bye"

Both of us together said, "Bye Mom"

After the call she said, "I love the way your parents handle things"

I said, "Yeah, even I love the way they raised Adithi and me. I'll tell you some instances. When I was studying 10th standard, I got attracted to a girl near our house. My scores were going down and I was becoming dull and restless. My dad identified these changes and one day he took me out to a restaurant and ordered for a beer for himself and asked if I wanted a beer.

I said, "Maybe yes" he ordered one for me and said, "This is not the official age to taste beer but temptations start at this age. The more you control the more you are tempted and tried so let's taste it. Moreover beer has less alcohol content when compared to other liquors. Everything is good when it is within limits"

The waiter got the beer and as we were taking it he said, "Arjun, I am glad that you are within the pass % in your studies but overall score is going down. What's troubling you?"

I didn't want to hide so I said, "Dad, I like the girl who is staying near our house. She is always on my mind"

He asked, "Is she studying in your class?"

I said, "No, she is doing her UG"

He said, "That's fine, age is not a matter at all. But you should think one thing. If your studies are going bad your future will be taken for a raid. Even if you are serious on this, it would be difficult for me to approach parents for her hand in marriage. Concentrate on your studies first, get a good job and then if you still have the same feeling towards that girl, I'll talk to her parents"

I felt relaxed and peaceful. After this we became good friends. I started concentrating on my studies and slowly I realized it's not love but infatuation that I had for that girl. (As I was saying this I felt a sense of possessiveness in Nethra's face) I said, "My dear tweety bird, you don't have to worry about all these things, I just want to be frank and open with you and expect the same from you too. No man is perfect and flawless; as a wife I think you need to know about my flaws than perfections"

She said, "Okay, but I'm feeling possessive. This feeling is new to me"

I said, "That's a good sign of love as long as it is within the limit"

I continued, I even told my dad about my interest to watch a porn movie when I was 17 yrs. He said, "I appreciate that you asked me. Proper sex education is needed now with raising AIDS and other STD diseases. It's natural and common to have these kind of desires at this age but I advice you, don't watch it from any movie hall. You'll become an animal and will lose respect for the other gender. You will see them as mere objects than as human beings. I'll get you an educational CD on that" and as said he did get me a CD and after that he asked me if it was useful and my comments on it too. This freedom and easiness offered by my parents had brought me till this level and I didn't go astray. They were able to guide Adithi and me in all walks of life and gave us the freedom to share and express our feelings.

Nethra said, "I wish I was born to them"

I said, "But if you're born to them, then I wouldn't have got this lovely wife. I'm happy and feel blessed to have you as my wife" saying this I kissed her and we started off with the "Hide & Seek game" and this term has become our code word from then on.

Our honeymoon was lovely. We flew back to India. Life was going on peacefully and happily. About 6 months later Nethra gave me the good news that we are gonna have a baby and I felt so happy. My mother took care of her very well, took her for regular checkups, scans and so on.

Nethra was very scared and she said, "I'm very much afraid" I said, "Don't be scared, stay calm and be comfortable. Check with mom if you have doubts" whatever I said and however I consoled her she grew restless day after day.

All of us in the family were happy until we found out that the umbilical cord is around the baby's neck during a check up in 8th month of pregnancy. The doctor said it's a risky procedure and the chances of survival are very less for the mother and the baby. Nethra got scared. She was admitted and there were few hours left for the operation.

She called me and said, "I'm scared, I think I'll not survive this operation"

My throat was shut with pain and grief with the thought of losing my loved one. I said, "No dear it is not gonna be like you think. You are gonna come back safely with a son or a daughter and we are gonna live happily"

She said, "If I die, I want you to marry Mithra"