Question

10 moles of $O_2$ gas are contained in a cylinder of 5 litre capacity. If the cylinder leakage into atmosphere (pressure is 1 atm and temperature is ${40}^{o}C$), then the work done by the gas will be

• A. $-1.59\text{kJ}$
• B. $-25.5\text{kJ}$
• C. $-3.27\text{kJ}$
• D. $-4.89\text{kJ}$

Answer 1

The correct option is B $-25.5\text{kJ}$

$V_1=5\text{litre}$
$P_{ext}=1\text{atm},T={40}^{\circ }C+273=313\text{K}$
$V_2=\frac{nRT}{P}=\frac{10\times 0.0821\times 313}{1}=256.97\text{litre}$
$W=-P_{ext}(V_2-V_1)$
$=-1(256.97-5)=-251.97\text{L atm}$
$=-251.97\times 101.3\text{J}$
$=-25524.8\text{J}=-25.5\text{kJ}$