Question

An open vessel at ${27}^{o}C$ is heated until ${\frac{3}{8}}^{th}$ of the air in it has been expelled. Assuming that the volume remains constant, calculate the temperature to which the vessel was heated.

• A. ${307}^{o}C$
• B. ${107}^{o}C$
• C. ${480}^{o}C$
• D. ${207}^{o}C$

Answer 1

The correct option is D ${207}^{o}C$

$PV=nRT$
at constant temperature and pressure , nT is constant

Given,
Initial temperature $T_1={27}^{o}C=27+273=300K$
initial moles = $n_1$

final moles = $n_1-\frac{3n_1}{8}=\frac{5n_1}{8}$
Using $n_1{T}_1=n_2{T}_2,T_2=\frac{n_1}{n_2}{T}_1=\frac{n}{(1-3/8)n}\times 300=\frac{n}{\left(5/8\right)n}\times 300=480K.$
$\therefore T_2={207}^{o}C.$