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JEE Main 2020 (3 Sep, Shift 2) · Thermodynamic Processes

Thermodynamic Processes question from JEE Main 2020 (3 Sep, Shift 2)

Q204JEE Main 2020 · 3 SEP · SHIFT 2Medium

Thermodynamic Processes

To raise the temperature of a certain mass of gas by 50oC at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100oC at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

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Answer: (a)

  1. Constant pressure: nCp×50=160⇒nCp=3.2nC_p \times 50 = 160 \Rightarrow nC_p = 3.2
  2. Constant volume: nCv×100=240⇒nCv=2.4nC_v \times 100 = 240 \Rightarrow nC_v = 2.4
  3. γ=3.22.4=43\gamma = \frac{3.2}{2.4} = \frac{4}{3}, and γ=1+2f⇒f=2γ−1=6\gamma = 1 + \frac{2}{f} \Rightarrow f = \frac{2}{\gamma - 1} = 6
  4. So the answer is (a) 6.
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