Question

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

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

Answer 1

Answer: (B)

$3573J$

Given: Temperature of a gas is ${37}^{0}C$ = 37+273.15=310.15 K

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,

$v_f=4v_i$

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

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

$W=nRT\ln 4$

$W=1\times 8.314\times 310.15\times \ln 4$

On solving we get,

$W=3574.68J$

The closest answer to 3574.62 J is 3573 J.

Hence, the correct option is (B).