Question

A ${27}^o$C one mole of an ideal gas is compressed isothermally and reversible from the pressure of $2$ atm to $10$ atm. The value of and $\Delta$E and q are:

$[R=2$ cal$]$

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

Answer 1

The correct option is A $0,-965.84$ cal

Isothermal (at constant temperature) and reversible work is given by,

$W=2.303nRTlog\frac{P_2}{P_1}$

$W=2.303\times \text{1 mol}\times \text{2 cal/mol/K}\times \text{300 K}log\frac{10}{2}$

$W=2.303\times 600\times log5$

$W=965.84$ cal.
$\Delta E=q+W$

At constant temperature, $\Delta E=0$

$0=q+W$

$q=-W=-965.84$ cal.

Hence, option $A$ is correct.