Question

At what temperature under constant volume, the pressure of a gas is double to that at $0^{\circ }\text{C}$ ?

• A. $273\text{K}$
• B. ${546}^{\circ }\text{C}$
• C. ${273}^{\circ }\text{C}$
• D. ${136.5}^{\circ }\text{C}$

Answer 1

The correct option is C ${273}^{\circ }\text{C}$

According to Gay-Lussac's law for constant volume, the pressure of given mass of gas is directly proportional to its absolute temperature.
i.e $P\propto T$

Given,
$P_2=2P_1{T}_1=0^{\circ }\text{C}=273\text{K}\therefore \frac{P_1}{T_1}=\frac{P_2}{T_2}\Rightarrow T_2=\frac{P_2}{P_1}\times T_1=2\times 273\text{K}=546\text{K}\Rightarrow T_2=(546-273{)}^{\circ }\text{C}\Rightarrow T_2={273}^{\circ }\text{C}$