Question

At $27℃$ , one mole of an ideal gas is compressed isothermally and reversibly from a pressure of $2$ atm to $10$ atm. The values of $\Delta \text{E}$ and $\text{q}$ are: $\left(\right.R=2$ and $log 5 = 0.698)$

• A. $0, \, -965.84 \, cal$
• B. $-965.84 \, cal, \, -865.58 \, cal$
• C. $+865.58 \, cal, \, -865.58 \, cal$
• D. $0, \, -865.58 \, cal$

Answer 1

Answer: (A)

$\text{W}=2.303 \, \text{n}\text{R}\text{T }\text{log} \frac{\text{p}_{2}}{\text{p}_{1}}$
$=2.303\times 1\times 2\times 300 \, \text{log} \frac{10}{2} = 965.84$
At constant temperature, $\Delta \text{E}=0$
$\Delta \text{E}=\text{q}+\text{W}$ ;
$\text{q}=-\text{W}=-965.84 \, \text{cal}$