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JEE Main 201910 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
10 January
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2019 · 10 January · Evening Shift · Physics · Kinetic Theory of Gases

2kg of a monoatomic gas is at a pressure of 4 × 10 ^ 4 N m ^ - 2 ....

2kg2kg of a monoatomic gas is at a pressure of 4×104Nm−24 \times {10}^{4}N{m}^{- 2}. The density of the gas is 8kgm−38kg{m}^{- 3}. What is the order of energy of the gas due to its thermal motion?

Options

  1. A105J{10}^{5}J
  2. B106J{10}^{6}J
  3. C104J{10}^{4}J
  4. D103J{10}^{3}J

Correct answer

C. 104J{10}^{4}J

Step-by-step solution

Internal energy is the energy due to thermal motion.

The internal energy of an ideal gas given by

U=f2nRTU = \dfrac{f}{2}nRT (for nmolesnmoles)

U=f2(PV)=f2×P×MρU = \dfrac{f}{2}\left(PV\right) = \dfrac{f}{2} \times P \times \dfrac{M}{ρ} (Since, f=3f = 3 for a monoatomic gas.)

U=32×4×104×28U = \dfrac{3}{2} \times 4 \times {10}^{4} \times \dfrac{2}{8}

=1.5×104J= 1.5 \times {10}^{4}J
So, the order of energy due to thermal motion is 104{10}^{4}

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