The ideal gas law states that:
[tex]pV=nRT[/tex]
where
p is the gas pressure
V is its volume
n is the number of moles
R is the gas constant
T is the absolute temperature
However, this equation can be also rewritten as
[tex]PV= \frac{2}{3}NK [/tex] (1)
where
N is the number of molecules in the gas, and K is the average kinetic energy of the molecules. Therefore, NK represents the total kinetic translational energy of the gas.
For the gas in our problem,
[tex]p=0.8 atm = 8.08 \cdot 10^4 Pa[/tex]
[tex]V=1.5 L =1.5 \cdot 10^{-3} m^3[/tex]
So, the total translational kinetic energy of the gas is (using eq.(1) )
[tex]NK= \frac{3}{2}pV= \frac{3}{2}(8.08 \cdot 10^4 Pa)(1.5 \cdot 10^{-3} m^3)=181.8 J [/tex]
