Question

Find the work done by a gas when it expands isothermally at ${37}^{o}C$ to four times its initial volume.

• A. 3753J
• B. 3573J
• C. 7533J
• D. 5375J

Answer 1

The correct option is B 3573J

Given: Temperature of a gas=${37}^{0}C$ = 310K

Solution: The total work done by a gas when it expands isothermally is given by,

$W=nRT\ln \frac{v_2}{v_1}$ (1)

According to question,

$v_2=4v_1$

So, substituting the value of $v_2$ in the equation (1) we get,

$W=nRT\ln \frac{4v_1}{v_1}$

$W=nRT\ln 4$

$W=1\times 8.314\times 310\times \ln 4$

On simplifying we get,

$W=3573J$

Hence, the correct option is (B).