An ideal monoatomic gas expands in such a manner that its pressure and volume can be related by equation $P{V}^{5/3} = cons\tan t$. During this process, the gas is 

(1) Heated

(2) Cooled

(3) Neither heated nor cooled

(4) First heated and then cooled

P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be -

1. 4 R

2. 2.5 R

3. 3 R

4. $\frac{4R}{3}$

Following figure shows on adiabatic cylindrical container of volume \(V_0\) divided by an adiabatic smooth piston (area of cross-section = \(A\)) in two equal parts. An ideal gas \(\left(\frac{C_P}{C_V}= \gamma\right)\) is at pressure \(P_1\) and temperature \(T_1\) in left part and gas at pressure \(P_2\) and temperature \(T_2\) in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be: (Suppose \(x\) = displacement of the piston)

          
1. \(P_2\)
2. \(P_1\)
3. \(\frac{P_1\left(\frac{V_0}{2}\right)^{\gamma}}{\left(\frac{V_0}{2}+ax\right)^{\gamma}}\)
4. \(\frac{P_2\left(\frac{V_0}{2}\right)^{\gamma}}{\left(\frac{V_0}{2}+ax\right)^{\gamma}}\)

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is 

(1) 30 K

(2) 18 K

(3) 50 K

(4) 42 K

A system goes from A to B via two processes I and II as shown in figure. If ΔU_I and ΔU_II are the changes in internal energies in the processes I and II respectively, then 

(1) ΔU_II > ΔU_I

(2) ΔU_II < ΔU_I

(3) ΔU_I = ΔU_II

(4) Relation between ΔU_I and ΔU_II can not be determined

A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is -

(1) 20 J

(2) – 20 J

(3) 400 J

(4) – 374 J

The P-V diagram shows seven curved paths (connected by vertical paths) that can be followed by a gas. Which two of them should be parts of a closed cycle if the net work done by the gas is to be at its maximum value 

(1) ac

(2) cg

(3) af

(4) cd

An ideal gas of mass m in a state A goes to another state B via three different processes as shown in figure. If Q₁, Q₂ and Q₃ denote the heat absorbed by the gas along the three paths, then -

(1) Q₁ < Q₂ < Q₃

(2) Q₁ < Q₂ = Q₃

(3) Q₁ = Q₂ > Q₃

(4) Q₁ > Q₂ > Q₃

Which of the following graphs correctly represents the variation of $\beta =-(dV/dP)/V$ with P for an ideal gas at constant temperature ?

(1)

(2)

(3)

(4)

A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are : $P_A=3\times {10}^{4}Pa,P_B=8\times {10}^{4}Pa$ and $V_A=2\times {10}^{-3}{m}^3,V_D=5\times {10}^{-3}{m}^3$. In process AB, 600 J of heat is added to the system and in process BC, 200 J of heat is added to the system. The change in internal energy of the system in process AC would be 

(1) 560 J

(2) 800 J

(3) 600 J

(4) 640 J