Question

An open vessel at ${27}^{o}C$ is heated until the three-fourths mass of the air in it has been expelled. Neglecting the expansion of the vessel, find the temperature to which the vessel has been heated.

• A. $T_2={723}^{o}C$
• B. $T_2={958}^{o}C$
• C. $T_2={927}^{o}C$
• D. None of these

Answer 1

Answer: (C)

$T_2={927}^{o}C$

No. of moles of air$=n$.

$\frac{3}{4}$ of original moles has expelled.

Remaining moles$=n(1-\frac{3}{4})$

$=\frac{n}{4}$.

At constant pressure & volume,

$n_1{T}_1=n_2{T}_2$.

$\Rightarrow \left(n\right)\left(300\right)=\left(\frac{n}{4}\right)\left(T_2\right)$

$\Rightarrow T_2=\left(300\right)\left(4\right)$

$=1200K$

$\Rightarrow T_2={927}^{\circ }C$.

$\therefore$ Temperature of vessel is ${927}^{\circ }C$.

Hence, (C) is the correct option.