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
![\Delta U = \frac{5}{2}nR\Delta T](https://tex.z-dn.net/?f=%5CDelta%20U%20%3D%20%5Cfrac%7B5%7D%7B2%7DnR%5CDelta%20T)
where:
n is the number of moles
R is the gas constant
is the change in temperature
For the gas in this problem:
n = 0.222 mol
![R=8.314 J/mol K](https://tex.z-dn.net/?f=R%3D8.314%20J%2Fmol%20K)
![\Delta T=12.0 K](https://tex.z-dn.net/?f=%5CDelta%20T%3D12.0%20K)
Substituting,
![\Delta U = \frac{5}{2}(0.222)(8.314)(12.0)=55.4 J](https://tex.z-dn.net/?f=%5CDelta%20U%20%3D%20%5Cfrac%7B5%7D%7B2%7D%280.222%29%288.314%29%2812.0%29%3D55.4%20J)
Now we can find the work done by the gas using the 1st law of thermodynamics:
![\Delta U = Q-W](https://tex.z-dn.net/?f=%5CDelta%20U%20%3D%20Q-W)
where:
Q = +80.5 J is the heat added to the gas
is the change in internal energy
W is the work done by the gas
And solving for W,
![W=Q-\Delta U = 80.5-(55.4)=25.1 J](https://tex.z-dn.net/?f=W%3DQ-%5CDelta%20U%20%3D%2080.5-%2855.4%29%3D25.1%20J)
And since it is positive, it means that the work is done BY the gas.
Learn more about thermodynamics:
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