Kinetic Theory and Thermodynamics
LIST–I  LIST–II  
P.  In process I  1.  Work done by the gas is zero 
Q.  In process II  2.  Temperature of the gas remains unchanged 
R.  In process III  3.  No heat is exchanged between the gas and its surroundings 
S.  In process IV  4.  Work done by the gas is 6P_{0}V_{0} 
An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here γ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. 

Column1  Column2  Column3 
(I) ${\mathrm{W}}_{1\to 2}=\frac{1}{\mathrm{\gamma}1}\left({\mathrm{P}}_{2}{\mathrm{V}}_{2}{\mathrm{P}}_{1}{\mathrm{V}}_{1}\right)$  (i) Isothermal  
(II) ${\mathrm{W}}_{1\to 2}={\mathrm{PV}}_{2}+{\mathrm{PV}}_{1}$  (ii) Isochoric  
(III) ${\mathrm{W}}_{1\to 2}=0$  (iii) Isobaric  
(IV) ${\mathrm{W}}_{1\to 2}=\mathrm{nRT}\mathrm{In}\frac{{\mathrm{V}}_{2}}{{\mathrm{V}}_{1}}$  (iv) Adiabatic 
Which of the following options is the only correct representation of a process in which ΔU = ΔQ – PΔV?
An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here γ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. 

Column1  Column2  Column3 
(I) ${\mathrm{W}}_{1\to 2}=\frac{1}{\mathrm{\gamma}1}\left({\mathrm{P}}_{2}{\mathrm{V}}_{2}{\mathrm{P}}_{1}{\mathrm{V}}_{1}\right)$  (i) Isothermal  
(II) ${\mathrm{W}}_{1\to 2}={\mathrm{PV}}_{2}+{\mathrm{PV}}_{1}$  (ii) Isochoric  
(III) ${\mathrm{W}}_{1\to 2}=0$  (iii) Isobaric  
(IV) ${\mathrm{W}}_{1\to 2}=\mathrm{nRT}\mathrm{In}\frac{{\mathrm{V}}_{2}}{{\mathrm{V}}_{1}}$  (iv) Adiabatic 
Which one of the following options is the correct combination?
An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here γ is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n. 

Column1  Column2  Column3 
(I) ${\mathrm{W}}_{1\to 2}=\frac{1}{\mathrm{\gamma}1}\left({\mathrm{P}}_{2}{\mathrm{V}}_{2}{\mathrm{P}}_{1}{\mathrm{V}}_{1}\right)$  (i) Isothermal  
(II) ${\mathrm{W}}_{1\to 2}={\mathrm{PV}}_{2}+{\mathrm{PV}}_{1}$  (ii) Isochoric  
(III) ${\mathrm{W}}_{1\to 2}=0$  (iii) Isobaric  
(IV) ${\mathrm{W}}_{1\to 2}=\mathrm{nRT}\mathrm{In}\frac{{\mathrm{V}}_{2}}{{\mathrm{V}}_{1}}$  (iv) Adiabatic 
Which one of the following options correctly represents a thermodynamics process that is used as a correction in the determination of the speed of sound in an ideal gas?
One mole of a monatomic ideal gas is taken along two cyclic processes E→F→G→E and E→F→H→E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

List I 

List II 
P. 
G→E 
1. 
160 P_{0}V_{0} ln2 
Q. 
G→H 
2. 
36 P_{0}V_{0} 
R. 
F→H 
3. 
24 P_{0}V_{0} 
S. 
F→G 
4. 
31 P_{0}V_{0} 
One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P −V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.
Column I 
Column II 

(A) 
Process AB 
(P) 
Internal energy decreases 
(B) 
Process B C 
(Q) 
Internal energy increases 
(C) 
Process C D 
(R) 
Heat is lost. 
(D) 
Process D A 
(S) 
Heated is gained 
(T) 
Work is done on the gas 
Column I

Column II


(A)  JK  (P) 
∆W > 0 
(B)  KL  (Q) 
∆Q < 0 
(C)  LM  (R)  ∆W < 0 
(D)  MJ  (S)  ∆Q > 0 