Question

An open vessel at $27{}^{\circ }C$ is heated until ${\frac{3}{8}}^{th}$ of the air in it has been expelled. Calculate the temperature at which the vessel was heated to.

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

Answer 1

The correct option is D $207{}^{\circ }C$

The volume of the vessel is constant and since it is open to the atomsphere, so is the pressure. Gas is expelled when it is heated, i.e., the number of moles $\left(n\right)$ of the gas changes to $(1-\frac{3}{8})\times n$.
Hence, using
$n_1{T}_1=n_2{T}_2\Rightarrow T_2=\frac{n_1}{n_2}{T}_1=\frac{n}{(1-\frac{3}{8})n}\times T_1=\frac{8}{5}\times 300=480K\therefore T_2=480-273=207{}^{\circ }C$