One kg of a diatomic gas is at a pressure of 8 × 10^4 N/m^2 . The density of the gas is 4 kg/m^3 . What is the energy of the gas due to its thermal mo - Physics MCQ AIEEE 2009 2026 | ExamTest.live

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One kg of a diatomic gas is at a pressure of 8 \times 1 0^{4} N/m^{2} . The density of the gas is 4 kg/m^{3} . What is the energy of the gas due to its thermal motion?

Solution & Step-by-step Explanation

The energy due to thermal motion is the internal energy U of the gas. For a diatomic gas, the degrees of freedom f = 5 .Internal energy U = \frac{f}{2} P V = \frac{5}{2} P V .Given: P = 8 \times 1 0^{4} N/m^{2}, Mass m = 1 kg, Density ρ = 4 kg/m^{3} .Volume V = \frac{m}{ρ} = \frac{1}{4} m^{3} . U = \frac{5}{2} \times (8 \times 1 0^{4}) \times \frac{1}{4} U = \frac{5}{2} \times 2 \times 1 0^{4} = 5 \times 1 0^{4} J

Try it yourself before checking the explanation above.

One kg of a diatomic gas is at a pressure of 8 \times 1 0^{4} N/m^{2} . The density of the gas is 4 kg/m^{3} . What is the energy of the gas due to its thermal motion?

3 \times 1 0^{4} J

5 \times 1 0^{4} J

6 \times 1 0^{4} J

7 \times 1 0^{4} J

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