The internal energy of the gas is 49,200 J
Explanation:
The internal energy of a diatomic gas, such as [tex]N_2[/tex], is given by
[tex]U=\frac{5}{2}nRT[/tex]
where
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
For the gas in this problem, we have:
n = 4.50 (number of moles)
R = 8.31 J/(mol·K) (gas constant)
[tex]T=253^{\circ} + 273 = 526 K[/tex] (absolute temperature)
Substituting, we find:
[tex]U=\frac{5}{2}(4.50)(8.31)(526)=49,200 J[/tex]
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