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Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ ( = Cₚ/C_v) are given respectively, by
- U = 5RT and γ = 7/5
- U = 5/2 RT and γ = 6/5
- U = 5RT and γ = 6/5
- U = 5/2 RT and γ = 7/5
Correct answer: U = 5/2 RT and γ = 7/5
Solution
The internal energy of an ideal gas is determined by its degrees of freedom, which for a diatomic gas includes three translational and two rotational degrees, leading to U = (5/2)RT. The ratio of specific heats, γ, is derived from the relationship between heat capacities, and for a diatomic gas, it is 7/5.
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