First Law of Thermodynamics

Q.

Which gas law is applied in refrigerators?

Q.

The internal energy of a given mass of gas in a system depends upon?

Q. A polyatomic gas $(\gamma =\frac{4}{3})$ is compressed to $\frac{1}{27}$ of its volume adiabatically and reversibly. If its initial pressure is $P_0$ its new pressure will be

1. $64P_0$
2. $21P_0$
3. $27P_0$
4. $81P_0$

Q. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma ,$ the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ under constant pressure $P$, is

1. $\frac{R}{(\gamma -1)}$
2. $pV$
3. $\frac{pV}{\gamma -1}$
4. $\frac{\gamma pV}{\gamma -1}$

Q. One mole of a monoatomic ideal gas expands adiabatically at initial temperature $T$ against a constant external pressure of $1atm$ from $1litreto3litres$. The final temperature of the gas is

1. $T$
2. ${\frac{T}{3}}^{\left(5R/2\right)}$
3. $T-\frac{2}{(1.5\times 0.082)}$
4. $T+\frac{2}{(1.5\times 0.082)}$

Q. One mole of an ideal gas is put through a series of changes as shown in the figure in which 1, 2, 3 mark the three stages of the system. Find the pressure (in bar) at three stages.

1. $\begin{array}{ccc}1& 2& 3\\ 1.107& 2.214& 1.107\end{array}$
2. $\begin{array}{ccc}1& 2& 3\\ 1.113& 2.226& 2.226\end{array}$
3. $\begin{array}{ccc}1& 2& 3\\ 2.214& 1.107& 2.214\end{array}$
4. $\begin{array}{ccc}1& 2& 3\\ 1.53& 3.06& 3.06\end{array}$

Q. $3000\text{J}$ of heat is given to a gas at constant pressure of $2\times {10}^5{\text{N/m}}^2$ If its volume increases by $10$ litres during the process find the change in the internal energy of the gas.

1. $-1000\text{J}$
2. $1000\text{J}$
3. $-2000\text{J}$
4. $2000\text{J}$

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : In evaporation of water, change in entropy is negative.
A : जल के वाष्पीकरण में, एन्ट्रॉपी में परिवर्तन ऋणात्मक है।

R : Evaporation of water is an endothermic process.
A : जल का वाष्पीकरण एक ऊष्माशोषी प्रक्रम है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. Match the column

$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ \text{(a)}& \text{Reversible cooling of an ideal gas at}& \text{(P)}& w=0;q<0;\Delta U<0\\ & \text{constant volume}& & \\ \text{(b)}& \text{Reversible isothermal expansion of an}& \text{(Q)}& w<0;q>0;\Delta U>0\\ & \text{ideal gas}& & \\ \text{(c)}& \text{Adiabatic expansion of non-ideal gas into}& \text{(R)}& w=0;q=0;\Delta U=0\\ & \text{vacuum}& & \\ \text{(d)}& \text{Reversible melting of sulphur at normal}& \text{(S)}& w<0;q>0;\Delta U=0\\ & \text{melting point}& & \end{array}$

1. a - P; b - S; c - R; d - Q
2. a - P; b - Q; c - S; d - R
3. a - R; b - S; c - Q; d - P
4. a - Q; b - R; c - S; d - P

Q. Heat given to a system is 35 J and work done by the system is 15 J. The change in the internal energy of the system will be:

1. 50 J
2. 20 J
3. 30 J
4. 40 J

Q. The P-V plot for three ideal gases for adiabatic expansion is given in the following figure. Curve A, curve B and curve C should correspond respectively to (Assuming same starting point X)

नीचे चित्र में तीन आदर्श गैसों के रूद्धोष्म प्रसार के लिए P-V आरेख दिया गया है। वक्र A, वक्र B तथा वक्र C क्रमशः किसके संगत होने चाहिए (माना प्रारम्भिक बिन्दु X समान है)?

1. CH₄, H₂, He
2. He, H₂, CH₄
3. H₂, He, CH₄
4. CH₄, He, H₂

Q. Density of an ideal gas is maximum at

किन परिस्थितियों पर एक आदर्श गैस का घनत्व अधिकतम होता है?

1. 4 atm and 300 K
   
   4 atm एवं 300 K
2. 2 atm and 450 K
   
   2 atm एवं 450 K
3. 3 atm and 300 K
   
   3 atm एवं 300 K
4. 2 atm and 300 K
   
   2 atm एवं 300 K

Q. Calculate the work done when one mole of gas is allowed to expand freely in vacuum.

1. 20 J
2. 0 J
3. 10 J
4. none of the above

Q. Five moles of a gas is put through a series of changes in a cyclic process as show in the graph.
Processes $A\to B,B\to C\text{and}C\to A$ respectively are:

1. Isochoric, Isobaric, Isothermal
2. Isobaric, Isochoric, Isothermal
3. Isothermal, Isobaric, Isochoric
4. Isochoric, Isothermal, Isobaric

Q. If $500cal$ of heat energy is added to a system and the system does $350cal$ of work on the surroundings, the internal energy change of the system is:

1. 150 cal
2. 850 cal
3. -150 cal
4. -850 cal

Q. A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas respectively will be:

1. $\frac{P}{2},T$
2. $\frac{P}{2},\frac{T}{2}$
3. $P,T$
4. $P,\frac{T}{2}$

Q.

How many joules are present in one calorie?

Q. Which of the following is the correct equation

1. $\Delta U=Q-W$
2. $W=\Delta U+Q$
3. $\Delta U=W+Q$
4. $Noneofthese$

Q.

A vessel contains 100 litres of a liquid $x$. Heat is supplied to the liquid in such a fashion that, Heat given = change in enthalpy. The volume of the liquid increases by 2 litres. If the external pressure is one atm, and 202.6 Joules of heat were supplied then, [ U - total internal energy ]

1. $\Delta U=0,\Delta H=0$

2. $\Delta U=+202.6J,\Delta H=+202.6J$

3. $\Delta U=-202.6J,\Delta H=-202.6J$

4. $\Delta U=0,\Delta H=+202.6J$

Q. If the amount of heat given to a system be $85J$ and the amount of work done by the system be $35J$, then the change in the internal energy of the system is

1. $50$
2. $120$
3. $55$
4. $160$

Q. Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non -expansion work is zero)

1. Adiabatic process: $\Delta U=-w$
2. Isochoric process: $\Delta U=q$
3. Cyclic process: $q=-w$
4. Isothermal process: $q=-w$

Q. Which of the following is the mathematical form of first law of thermodynamics?

1. $\Delta U=W$ for an adiabatic process
2. $\Delta U=q$ for an isochoric process
3. $q=-W$ for an isothermal process
4. All of the above

Q. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma ,$ the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ under constant pressure $P$, is

1. $\frac{R}{(\gamma -1)}$
2. $pV$
3. $\frac{pV}{\gamma -1}$
4. $\frac{\gamma pV}{\gamma -1}$

Q. In an isochoric process the increase in internal energy is

1. Equal to the heat absorbed
2. Equal to the heat evolved
3. Equal to the work done

4. Equal to the sum of the heat absorbed and work done

Q. The standard enthalpy of formation of $C{F}_{2}ClC{F}_{2}Cl\left(g\right)$ $\left({\Delta }_f{H}_{300}^{\circ }\right)$ at $1\text{bar}$ and $300\text{K}$ from its constituent elements in their standard states is $-900{\text{kJ mol}}^{-1}$. (Given, $R=8.3{\text{J K}}^{-1}{\text{mol}}^{-1}$)
The standard internal energy of formation $\left({\Delta }_f^{\circ }{U}_{300}\right)$ at the same pressure and temperature is:

1. $-905.02{\text{kJ mol}}^{-1}$
2. $-895.02{\text{kJ mol}}^{-1}$
3. $895.02{\text{kJ mol}}^{-1}$
4. $905.02{\text{kJ mol}}^{-1}$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

For the given process, select the correct statement(s).

दिए गए प्रक्रम के लिए सही कथन/कथनों का चयन कीजिए।

1. Process I → II is isochoric
   
   प्रक्रम I → II समआयतनी है
2. Process II → III is isobaric
   
   प्रक्रम II → III समदाबी है
3. Process I → II is isothermal
   
   प्रक्रम I → II समतापीय है
4. Work done in process II → III is zero and the process is isochoric
   
   प्रक्रम II → III में किया गया कार्य शून्य है तथा प्रक्रम समआयतनी है

Q. A certain volume of dry gas at NTP is expanded reversibly to three times its volume adibatically. Calculate the final temperature and pressure assuming ideal behaviour.$\frac{C_p}{C_v}$ for air = 1.4.

1. 176 K, 0.215 atm
2. 154 K, 1.52 atm
3. 254 K, 0.568 atm
4. 454 K, 0.684 atm

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

Select correct statement(s) among the following in context to Gibbs free energy change (ΔG) of a chemical reaction

रासायनिक अभिक्रिया की गिब्स मुक्त ऊर्जा परिवर्तन (ΔG) के विषय में निम्नलिखित में से सही कथन/कथनों का चयन कीजिए।

1. Sign of ΔG helps in prediction of the spontaneity of the chemical reaction
   
   (ΔG) का चिन्ह रासायनिक अभिक्रिया की स्वतः प्रवर्तिता के निर्धारण में सहायक होता है
2. Its magnitude allows to predict the useful work that could be extracted from it
   
   इसका परिमाण उस उपयोगी कार्य का निर्धारण करता है जो इससे प्राप्त हो सकता है
3. At equilibrium the free energy of the system is minimum
   
   साम्य पर निकाय की मुक्त ऊर्जा न्यूनतम होती है
4. At equilibrium the free energy of the system is maximum
   
   साम्य पर निकाय की मुक्त ऊर्जा अधिकतम होती है

Q. What is the change in internal energy when a gas contracts from $377$ mL to $177$ mL under a constant pressure of 2 atm, while at the same time being cooled by removing $124J$ heat?
[Take: $1Latm$ = $100J$]

1. $-24J$
2. $-84J$
3. $-164J$
4. $-24J$

Q. Match the column

$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ \text{(a)}& \text{Reversible cooling of an ideal gas at}& \text{(P)}& w=0;q<0;\Delta U<0\\ & \text{constant volume}& & \\ \text{(b)}& \text{Reversible isothermal expansion of an}& \text{(Q)}& w<0;q>0;\Delta U>0\\ & \text{ideal gas}& & \\ \text{(c)}& \text{Adiabatic expansion of non-ideal gas into}& \text{(R)}& w=0;q=0;\Delta U=0\\ & \text{vacuum}& & \\ \text{(d)}& \text{Reversible melting of sulphur at normal}& \text{(S)}& w<0;q>0;\Delta U=0\\ & \text{melting point}& & \end{array}$

1. a - P; b - S; c - R; d - Q
2. a - P; b - Q; c - S; d - R
3. a - R; b - S; c - Q; d - P
4. a - Q; b - R; c - S; d - P