Question

One mole of an ideal gas is kept enclosed under a light piston (area=${10}^{-2}{m}^2$) connected by a compressed spring (spring constant $100N/m$).

The volume of gas is ${0.83}^3$ and its temperature is $100K$. The gas is heated so that it compresses the spring further by $0.1m$. The work done by the gas in the process is: (Take $R=8.3J/K$-mole and suppose there is no atmosphere).

• A. $3J$
• B. $6J$
• C. $9J$
• D. $1.5J$

Answer 1

The correct option is D $1.5J$

The pressure is given as,

$P=\frac{RT}{V}$

$=\frac{8.3\times 100}{0.83}$

$=1000N/m^2$

The force is given as,

$F=PA$

$=1000\times {10}^{-2}$

$=10N$

The kinetic energy is given as,

$K=\frac{1}{2}k{x}^2$

$=\frac{1}{2}\times 100\times {\left(0.1\right)}^2$

$=0.5J$

The total work done is given as,

$W=K+F\times s$

$=0.5+10\times 0.1$

$=1.5J$

Thus, the work done by the gas process is $1.5J$.