Question

A vertical cylinder with a massless piston filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature $300K.$ The amount of work done in increasing the volume two times is $(R=\frac{25}{3}\text{J/mol-K},\ln 2=0.7)$

• A. $1750J$
• B. $2500J$
• C. $750J$
• D. $4250J$

Answer 1

The correct option is C $750J$


Let the amount of work done in increasing the volume of gas two times be $W_{ext}$. Now there is work done by the gas $W_g$ and work done by the atmospheric pressure $W_A$.
Since the piston does not have K.E, we can say:
$W_{ext}+W_g+W_A=0$

For isothermal process,
Work done by the gas $W_g=nRT\ln \frac{V_2}{V_1}$
$W_g=1\times \frac{25}{3}\times 300\times \ln 2$
$W_g=1750J$

The work done by the atmospheric pressure ($P_0$) is:
$W_A=-P_0(V_2-V_1)=-P_0(2V_1-V_1)W_A=-P_0{V}_1=-nRT=-\frac{25}{3}\times 300W_A=-2500J$

So the external work done to increase the volume of gas would be,
$W_{ext}=-W_g-W_A{W}_{ext}=-(1750-2500)=750J$