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

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Solution

According to Charles Law
Volume of a gas is directly proportional to the temperature at constant pressure and number of moles.
$V_{1} \propto T_{1}$ $V_{2} \propto T_{2}$
$\frac{V_{1}}{V_{2}} = \frac{T_{1}}{T_{2}} ⟶ (1)$
If % change in volume is $10$ %
$\Rightarrow \frac{V_{2} - V_{1}}{V_{1}} \times 100 = 10$
$\Rightarrow \frac{V_{2} - V_{1}}{V_{1}} = 0.1$
$\Rightarrow V_{2} = 1.1 V_{1}$
On putting the value of $1 / 2$ in equation (1)
$\Rightarrow \frac{V_{1}}{1.1 V_{1}} = \frac{T_{1}}{T_{2}}$
Thus $T_{2} = 1.1 T_{1}$
% change in temperature= $\frac{T_{2} - T_{1}}{T_{1}} \times 100 = \frac{1.1 T_{1} - T_{1}}{T_{1}} \times 100$
$Δ T = 10$ %

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