Question

Calculate the % change in temperature if % change in volume of heat is $10$%.

Answer 1

According to Charles Law

Volume of a gas is directly proportional to the temperature at constant pressure and number of moles.

$V_1\propto T_1$ $V_2\propto T_2$

$\frac{V_1}{V_2}=\frac{T_1}{T_2}⟶\left(1\right)$

If % change in volume is $10$%

$\Rightarrow \frac{V_2-V_1}{V_1}\times 100=10$

$\Rightarrow \frac{V_2-V_1}{V_1}=0.1$

$\Rightarrow V_2=1.1V_1$

On putting the value of $1/2$ in equation (1)

$\Rightarrow \frac{V_1}{1.1V_1}=\frac{T_1}{T_2}$

Thus $T_2=1.1T_1$

% change in temperature= $\frac{T_2-T_1}{T_1}\times 100=\frac{1.1T_1-T_1}{T_1}\times 100$

$\Delta T=10$%