Question

A mass m is on top of a platform that is supported by gas in a cylinder of cross-sectional area A, as shown.

Answer 1

Answer:

$\frac{mg}{mg+pA}$

Explanation:

1)Image of proper question is attached .

Now, we have mass ' m ' raise to height 'h' when temperature of the gas is increased .

Hence,

Gain in potential energy of the mass is given by : mgh

Now,

Work is done by the gas to overcome Atmospheric pressure and weight of the mass.

2) To Overcome Atmospheric pressure,balanced force:

$W_1=\int\:pdV=p*V=p*A*h$

To Overcome weight,balanced force:

$W_2=mgh$

Hence,

Net Work is given by

$W=W_1+W_2\\ \\=pAh+mgh$

3) But , we require

Ratio of Gain in potential energy of mass 'm' and Work done by the gas

Required Value: $\frac{mgh}{mgh+pAh}=\frac{mg}{mg+pA}$