Question

An open flask contains air at ${27}^{\circ }C$. To what temperature it must be heated to expel one - fourth of the volume?

• A. ${123}^{\circ }C$
• B. ${127}^{\circ }C$
• C. ${133}^{\circ }C$
• D. ${145}^{\circ }C$

Answer 1

The correct option is B

${127}^{\circ }C$

Let volume of flask = 1 L
Volume $\alpha$ number of moles initially (n1)
Volume of air expelled $\frac{1}{4}L\propto \frac{1}{4}{n}_1$
Number of moles left in the flask = $(n_1-\frac{1}{4}{n}_1)=\frac{3}{4}{n}_1$

Ideal gas equation:
$P_1{V}_1=n_{1}R{T}_1...\left(i\right),P_1{V}_1=n_{2}R{T}_2...\left(ii\right)$
(Since P and V of the flask are constant)
From Eqs. (i) and (ii)
$n_1{T}_1=n_2{T}_2$
$n_1\times 300=\frac{3}{4}{n}_1{T}_2$
$T_2=300\times \frac{4}{3}=400K={127}^{\circ }C$