Question

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

• A. $20.48g$
• B. $204.8g$
• C. $20.48kg$
• D. $2048kg$

Answer 1

The correct option is D $2048kg$

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

$M=2048.469kg$ or $2048kg$

Hence, option D is correct.