A diatomic gas which has initial volume of 10 litre is isothermally compressed to 1 / 15^th of its original volume where initial pressure is 10^5 Pascal . If temperature is 27^° C then find the work done by gas.

Correct answer: (A) -2.70 × 10^3 ~J. W =n R T ln (V_2/V_1 )=P_0 V_0 ln (V_2/V_1 ) =10^5 × 10 × 10^-3 ln (1/15 ) =-2.70 × 10^3 ~J

Q94 / 180 · AIIMS 2018 (26 May) · Physics

A diatomic gas which has initial volume of 10 litre is isothermally compressed to $1 / 15^{\text {th }}$ of its original volume where initial pressure is $10^5 \mathrm{Pascal}$. If temperature is $27^{\circ} \mathrm{C}$ then find the work done by gas.

Correct answer
A
$-2.70 \times 10^3 \mathrm{~J}$
B
$2.70 \times 10^3 \mathrm{~J}$
C
$-1.35 \times 10^3 \mathrm{~J}$
D
$1.35 \times 10^3 \mathrm{~J}$

Solution

$\begin{aligned} W & =n R T \ln \left(\frac{V_2}{V_1}\right)=P_0 V_0 \ln \left(\frac{V_2}{V_1}\right) \\ & =10^5 \times 10 \times 10^{-3} \ln \left(\frac{1}{15}\right) \\ & =-2.70 \times 10^3 \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'A'.

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