The work done by the gas is 25.1 J
Explanation:
The change in internal energy of a diatomic gas is given by the equation
[tex]\Delta U = \frac{5}{2}nR\Delta T[/tex]
where:
n is the number of moles
R is the gas constant
[tex]\Delta T[/tex] is the change in temperature
For the gas in this problem:
n = 0.222 mol
[tex]R=8.314 J/mol K[/tex]
[tex]\Delta T=12.0 K[/tex]
Substituting,
[tex]\Delta U = \frac{5}{2}(0.222)(8.314)(12.0)=55.4 J[/tex]
Now we can find the work done by the gas using the 1st law of thermodynamics:
[tex]\Delta U = Q-W[/tex]
where:
Q = +80.5 J is the heat added to the gas
[tex]\Delta U = +55.4 J[/tex] is the change in internal energy
W is the work done by the gas
And solving for W,
[tex]W=Q-\Delta U = 80.5-(55.4)=25.1 J[/tex]
And since it is positive, it means that the work is done BY the gas.
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