Question

In the arrangement shown in the figure, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure $P_o$ (greater than atmospheric pressure $P_a$). A spring of force constant $k$ is initially unstrecthed. The piston of mass $m$ and ares $s$ is frictionless. In equilibrium, the piston rises up by distance $x_o$, then

• A. final pressure of the gas is $P_a+\frac{k{x}_o}{s}+\frac{mg}{s}$
• B. work done by the gas $\frac{1}{2}k{x}_o^2+mg{x}_o$
• C. Internal energy of the gas decreases
• D. all the above

Answer 1

Answer: (A), (C)

The correct options are
A final pressure of the gas is $P_a+\frac{k{x}_o}{s}+\frac{mg}{s}$
C Internal energy of the gas decreases

At equilibrium, the forces acting on the piston is given by
$Ps=P_a+k{x}_o+mg$
$P=P_a+\frac{k{x}_o}{s}+\frac{mg}{s}$

Work done by the gas,
$\text{W.d}=Ps{x}_o=P_{a}s{x}_o+mg{x}_o+\frac{1}{2}k{x}_o^2$

Internal energy decreases as the gas does some work to push the piston