Question

When the temperature of a gas, contained in a closed vessel is increased by ${25}^o$, its pressure increases by $10\%$. The original temperature of the gas was approximately:

• A. ${500}^{0}C$
• B. ${250}^{0}C$
• C. ${227}^{0}C$
• D. ${50}^{0}C$

Answer 1

The correct option is B ${250}^{0}C$

Given,

Percentage increase in pressure is $10$%

Increase in temperature is ${25}^{o}C$

For constant volume,

$P\alpha T$

$\frac{P_2}{P_1}=\frac{T_2}{T_1}$

$\Rightarrow \frac{1.01P_1}{P_1}=\frac{(T_1+25)}{T_1}$

$\Rightarrow T_1=\frac{25}{0.1}=250{}^{o}C$

Hence, initial temperature is ${250}^{o}C$