Question

When temperature of an ideal gas is increased from ${27}^{\circ }\text{C}$ to ${227}^{\circ }\text{C}$ keeping its mass and pressure constant, then volume of the gas will be increased by

• A. $33.33\%$
• B. $66.66\%$
• C. $30\%$
• D. $60\%$

Answer 1

The correct option is B $66.66\%$


According to Charle's law,
For constant pressure, the volume of the given mass of gas is directly propotional to its temperature.
$V\propto T$
$\therefore \frac{V_2}{V_1}=\frac{T_2}{T_1}\text{Given}:T_1={27}^{\circ }\text{C}=(27+273)\text{K}=300\text{K}{T}_2={227}^{\circ }\text{C}=(227+273)\text{K}=500\text{K}\Rightarrow \frac{V_2}{V_1}=\frac{500\text{K}}{300\text{K}}=\frac{5}{3}\Rightarrow \frac{V_2}{V_1}=\frac{5}{3}\Rightarrow \frac{V_2-V_1}{V_1}\times 100=\frac{5-3}{3}\times 100=66.66\%$