Question

Pressure of gas contained in a closed vessels is increased by $0.4\%$, when heated by ${}^{o}C$. Calculate its final temperature. Assume ideal nature.

Answer 1

Initial pressure in the vessel $1atm$ $=P_1$

After increasing $0.4$% the pressure $P_2=1.004P_1$.

and $T_2=T_1+1$

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\Rightarrow \frac{P_1}{T_1}=\frac{P_2}{T_2}$ (As volume constant).

$T_1=\frac{P_1{T}_2}{P_2}$

$=\frac{P_1(T_1+1)}{1.004P_1}$

$T_1=\frac{T_1+1}{1.004}$

$T_1=\frac{1}{0.004}=250K$