JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Topic Test - Kinetic Theory of Gases

The value of \[{{C}_{p}}-{{C}_{v}}=1.00R\] for a gas in state A and \[{{C}_{p}}-{{C}_{v}}=1.06R\] in another state. If \[{{P}_{A}}\] and \[{{P}_{B}}\] denote the pressure and \[{{T}_{A}}\] and \[{{T}_{B}}\] denote the temperatures in the two states, respectively, then

A) \[{{P}_{A}}={{P}_{B}},\,{{T}_{A}}>{{T}_{B}}\]

B) \[{{P}_{A}}>{{P}_{B}},\,{{P}_{A}}={{T}_{B}}\]

C) \[{{P}_{A}}<{{P}_{B}},\,{{P}_{A}}>{{P}_{B}}\]

D) \[{{P}_{A}}>{{P}_{B}},\,{{T}_{A}}<{{T}_{B}}\]

Correct Answer: C

Solution :

[c] For state \[A,\,{{C}_{p}}-{{C}_{v}}=R,\] i.e., the gas behaves as ideal gas.

For state \[B,\,{{C}_{p}}-{{C}_{v}}=1.06\,R(\ne R),\] i.e., the gas does not behave like ideal gas.

And we know that at high temperature and at low pressure nature of gas may be ideal.

So we can say that \[{{P}_{A}}<{{P}_{B}}\] and \[{{T}_{A}}>{{T}_{B}}\]