Question

One mole of an ideal gas is compressed from 0.5 lit to 0.25 lit. During the compression, $23.04\times {10}^2$ J of work is done on the gas and heat is removed to keep the temperature of the gas constant at all times. Find the temperature of the gas. (Take universal gas constant $R=8.31Jmo{l}^{-1}{K}^{-1}$)

Answer 1

Given : Work of compression $W_{com}=-23.04\times {10}^2$ J

Initial volume $V_1=0.5$ L

Final volume $V_2=0.25$ L

Let the temperature of the gas be $T$

As the temperature is constant all the time, thus the gas is compressed isothermally.

Workdone in isothermal compression $W_{com}=nRTln(\frac{V_2}{V_1})$

$\therefore$ $-2304=1\times 8.31\times Tln(\frac{0.25}{0.5})$

$-2304=1\times 8.31\times T\times (-ln2)$ $(ln2=0.693)$

$⟹T=400K$