Question

$5$ moles of an ideal gas expand isothermally and reversibly from a pressure of $10atm$ to $2atm$ at $300K$. What is the largest mass which can be lifted through a height of $1$ metre in this expansion?

• A. $2048.5kg$
• B. $20.08kg$
• C. $2048.5gm$
• D. $20.08gm$

Answer 1

The correct option is A $2048.5kg$

Work done by the system(w)

= $-nRT{\log }_e\frac{P_1}{P_2}=-2.303nRT\log \frac{P_1}{P_2}$

$=-2.303\times 5\times 8.314\times 300\log \frac{10}{2}=-20.075\times {10}^{3}J$

Let $M$ be the mass which can be lifted through a height of $1m$.

Work done in lifting the mass $=Mgh=M\times 9.8\times 1J$

So, $M\times 9.8=20.075\times {10}^3$

$M=2048.469kg$