Question

2.0m³ of gas is stored at a pressure of 12 atmosphere and a temperature of -23⁰cwhat volume would that same gas occupy at 27⁰c and atmosphere pressure?

Answer 1

Given that in the first case,

the volume of the gas is

$V_1=2m^3$

The pressure of the gas is

$P_1\text{ = 12 atm}$

The temperature of the gas is

$\begin{gathered} T_1=-23^{\circ\text{ }}C+273.15 \\ =250.15\text{ K} \end{gathered}$

In the second case,

the pressure of the gas is

$P_2=\text{ 1 atm}$

The temperature of the gas is

$\begin{gathered} T_2=27^{\circ}C+273.15 \\ =\text{ 300.15 K} \end{gathered}$

We have to find the volume, V2.

The volume v2 can be calculated as

$\begin{gathered} \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2} \\ V_2=\text{ }\frac{P_1V_1T_2}{P_2T_1} \\ =\frac{12\times2\times(250.15)}{1\times(300.15)} \\ =20.00m^3 \end{gathered}$