$ 2 \mathrm{~kg} $ of a monoatomic gas is at a pressure of $ 4 \times 10^{4} \mathrm{~N} \mathrm{~m}^{-2} $. The density of the gas is $ 8 \mathrm{~kg} \mathrm{~m}^{-3} $. What is the order of energy of the gas due to its thermal motion?

Question

$ 2 \mathrm{~kg} $ of a monoatomic gas is at a pressure of $ 4 \times 10^{4} \mathrm{~N} \mathrm{~m}^{-2} $. The density of the gas is $ 8 \mathrm{~kg} \mathrm{~m}^{-3} $. What is the order of energy of the gas due to its thermal motion?, $ 10^{5} \mathrm{~J} $, $ 10^{6} \mathrm{~J} $, $ 10^{4} \mathrm{~J} $, $ 10^{3} \mathrm{~J} $

MARKS App · Accepted Answer

Internal energy is the energy due to thermal motion. The internal energy of an ideal gas given by U = f 2 n R T (for n moles ) U = f 2 P V = f 2 × P × M ρ (Since, f = 3 for a monoatomic gas.) U = 3 2 × 4 × 10 4 × 2 8 = 1.5 × 10 4 J So, the order of energy due to thermal motion is 10 4

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