Question

The initial temperature of a gas is ${100}^{\circ }C.$ The gas is contained in closed vessel. If the pressure of the gas is increased by $5\%,$ calculate the increase in temperature of the gas:

• A. $2^{\circ }C$
• B. $4^{\circ }C$
• C. $1^{\circ }C$
• D. $5^{\circ }C$

Answer 1

The correct option is D $5^{\circ }C$

We know that: $PV=RT$

Given: $P_2=P_1+5\%$ of $P_1,V=constant$

Volume of gas is constant
By ideal gas equation we can say

$P\propto T$

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

Let $T_2=T_1+\Delta T$

$\frac{100}{(100+\Delta T)}=\frac{P}{1.05P}$

$105P=100:P+P\times \Delta T$

$\frac{5P}{P}=\Delta t=5^{\circ }C$

$\text{Final answer: (d)}$