Question

Keeping the pressure fixed at what temperature the volume of a gas becomes double of the original volume at zero degree celsius

Answer 1

Charles' Law states that the volume of a gas is directly proportional to temperature at constant pressure.

$\longrightarrow\sf{V\propto T}$

Therefore,

$\longrightarrow\sf{\dfrac{V_2}{V_1}=\dfrac{T_2}{T_1}\quad\quad\dots(1)}$

Here initial temperature is,

$\longrightarrow\sf{T_1=0^{\circ}C=273\ K}$

Here final volume of the gas becomes double the initial volume.

$\longrightarrow\sf{V_2=2V_1}$

$\longrightarrow\sf{\dfrac{V_2}{V_1}=2}$

From (1),

$\longrightarrow\sf{\dfrac{T_2}{T_1}=2}$

$\longrightarrow\sf{T_2=2T_1}$

$\longrightarrow\sf{T_2=2\times273\ K}$

$\longrightarrow\underline{\underline{\sf{T_2=546\ K}}}$

$\longrightarrow\underline{\underline{\sf{T_2=273^{\circ}C}}}$

Hence the volume of the gas becomes double at $\bf{273^{\circ}C}.$