The gas releases an amount of heat equal to -225 J
Explanation:
The change in internal energy of a diatomic gas is given by:
[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 this gas we have:
n = 0.235 mol
[tex]R=8.31 J/mol K[/tex]
[tex]\Delta T = -88 K[/tex]
So, the change in internal energy of the gas is
[tex]\Delta U = \frac{5}{2}(0.235)(8.31)(-88)=-430 J[/tex]
Now we can use the 1st law of thermodynamics to find the heat absorbed/released by the gas:
[tex]\Delta U = Q - W[/tex]
where
Q is the heat absorbed by the gas
W is the work done by the gas
Here we have:
[tex]\Delta U = -430 J[/tex]
[tex]W=205 J[/tex]
Solving for Q, we find:
[tex]Q=\Delta U + W = -430 +205=-225 J[/tex]
Where the negative sign means the heat has been released by the gas.
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