If 32 gm of \(O_2\)${\mathrm{}}_{}$ at \(27^{\circ}\mathrm{C}\) is mixed with 64 gm of \(O_2\)${\mathrm{}}_{}$ at \(327^{\circ}\mathrm{C}\) in an adiabatic vessel, then the final temperature of the mixture will be:
1. \(200^{\circ}\mathrm{C}\)
2. \(227^{\circ}\mathrm{C}\)
3. \(314.5^{\circ}\mathrm{C}\)
4. \(235.5^{\circ}\mathrm{C}\)$\mathrm{}$

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure.

The change in internal energy of the gas during the transition is

1. 20 kJ
 

2. -20 kJ
 

3. 20 J
 

4. -12 kJ

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of C_P/C_V for the gas is equal to:

If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V constant pressure p, is 

(1) $R/(\gamma -1)$

(2) pV

(3) $pV/(\gamma -1)$

(4) $\gamma pV/(\gamma -1)$

The specific heat of a gas in an isothermal process is: