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JEE Main 2009
Exam
JEE Main
Year
2009
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2009 · Physics · Kinetic Theory of Gases

One kg of a diatomic gas is at a pressure of 8 × 10^4 ~N / m^2 ....

One kg of a diatomic gas is at a pressure of 8×104 N/m28 \times 10^4 \mathrm{~N} / \mathrm{m}^2. The density of the gas is 4 kg/m−34 \mathrm{~kg} / \mathrm{m}^{-3}. What is the energy of the gas due to its thermal motion?

Options

  1. A3×104 J3 \times 10^4 \mathrm{~J}
  2. B5×104 J5 \times 10^4 \mathrm{~J}
  3. C6×104 J6 \times 10^4 \mathrm{~J}
  4. D7×104 J7 \times 10^4 \mathrm{~J}

Correct answer

B. 5×104 J5 \times 10^4 \mathrm{~J}

Step-by-step solution

Thermal energy corresponds to internal energy Mass =1 kg=1 \mathrm{~kg} density =8 kg/m3⇒=8 \mathrm{~kg} / \mathrm{m}^3\Rightarrow Volume = mass  density =18 m3=\frac{\text{ mass }}{\text{ density }}=\frac{1}{8} \mathrm{~m}^3 Pressure =8×104 N/m2∴=8 \times 10^4 \mathrm{~N} / \mathrm{m}^2\therefore Internal Energy =52P×V=5×104 J=\frac{5}{2} \mathrm{P} \times \mathrm{V}=5 \times 10^4 \mathrm{~J}
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