# If 60 liters of hydrogen gas at 546 K is cooled to 273 K at constant pressure, what will the new volume of the gas be?

Jan 21, 2016

Data:-
Initial Volume$= {V}_{1} = 60 l i t e r$
Initial Temperature$= {T}_{1} = 546 K$
Final Temperature$= {T}_{2} = 273 K$
Final Vloume=V_2=??
Sol:-

Since the pressure is constant and the question is asking about temperature and volume, i.e,
${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

$\implies {V}_{2} = \frac{{V}_{1} \cdot {T}_{2}}{T} _ 1 = \frac{60 \cdot 273}{546} = \frac{60}{2} = 30 l i t e r$

$\implies {V}_{2} = 30 l i t e r$

Hence the new volume of the gas is $30 l i t e r$