When an ideal monoatomic gas is heated at constant pressure, fraction of heat energy supplied which increases the internal energy of gas, is 

(1) $\frac{2}{5}$

(2) $\frac{3}{5}$

(3) $\frac{3}{7}$

(4) $\frac{3}{4}$

When an ideal gas (γ = 5/3) is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work ?

1. 40 %

2. 30 %

3. 60 %

4. 20 %

Two samples A and B of a gas initially at the same pressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically). The final pressure of A is 

(1) Greater than the final pressure of B

(2) Equal to the final pressure of B

(3) Less than the final pressure of B

(4) Twice the final pressure of B

Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4V and then compressed adiabatically to volume V. The final pressure of gas will be [Given : $\gamma =1.5 ]$-

(1) 1P

(2) 2P

(3) 4P

(4) 8P

A thermally insulated rigid container contains an ideal gas heated by a filament of resistance 100 Ω through a current of 1A for 5 min . Then change in internal energy is -

(1) 0 kJ

(2) 10 kJ

(3) 20 kJ

(4) 30 kJ

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62°C, the efficiency of the engine is doubled. The temperatures of the source and sink are -

(1) 80°C, 37°C

(2) 95°C, 28°C

(3) 90°C, 37°C

(4) 99°C, 37°C

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