Question

An ideal gas has initial volume V
pressure P and absolute temperature
T. The gas first undergoes an isobaric
expansion so that its volume becomes
four times of its initial volume and then
undergoes an isothermal compression to
restore its volume to its original value
The final pressure and absolute
temperature are respectively
(A) 4P.2T
(E) 2P. 4T
(C) 4P. 47
(D) 4P, T/4​

Answer 1

Given:

Initial volume = V

Initial pressure = P

Initial temperature = T

To find:

The final pressure and absolute temperature

Calculation:

Firstly, the gas undergoes isobaric expansion and the volume becomes four time its original volume. So P₁=P, V₁=4V

      $\frac{V}{T} = \frac{V_1}{T_1}$

      $\frac{V}{T} = \frac{4V}{T_1}\Rightarrow T_1=4T$

Secondly, the gas undergoes undergoes isothermal compression and the volume restores to its original volume, So T₂=T₁, V₂=V

     $P_1V_1=P_2V_2$

     $P\times 4V=P_2\times V$

     $P_2=4P$

The final values of Pressure, Temperature and Volume are 4P, V, 4T

Final answer:

The final pressure and absolute temperature are 4P, 4T [option(c)]