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Heat and Thermodynamics question

2022 · 26 Jul · Shift 2 · Q50
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Heat and Thermodynamics question

2022 · 26 Jul · Shift 2 · Q50

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A gas has nnn degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :
  1. A
    nn+2\frac{n}{n+2}n+2n​
  2. B
    n+2n\frac{n+2}{n}nn+2​
  3. C
    n2n+2\frac{n}{2n+2}2n+2n​
  4. D
    nn−2\frac{n}{n-2}n−2n​
View written solutionFree

Correct answer: A

  1. For an ideal gas with nnn degrees of freedom, the molar specific heat at constant volume is CV=n2RC_V = \frac{n}{2}RCV​=2n​R because each degree of freedom contributes 12R\frac{1}{2}R21​R per mole.

  2. The molar specific heat at constant pressure is CP=CV+R=n2R+R=n+22R.C_P = C_V + R = \frac{n}{2}R + R = \frac{n+2}{2}R.CP​=CV​+R=2n​R+R=2n+2​R.

  3. The question asks for the ratio of specific heat at constant volume to specific heat at constant pressure: CVCP=n2Rn+22R=nn+2.\frac{C_V}{C_P} = \frac{\frac{n}{2}R}{\frac{n+2}{2}R} = \frac{n}{n+2}.CP​CV​​=2n+2​R2n​R​=n+2n​.

  4. Now compare with the options:

  • A: nn+2\frac{n}{n+2}n+2n​ ✓
  • B: n+2n\frac{n+2}{n}nn+2​
  • C: n2n+2\frac{n}{2n+2}2n+2n​
  • D: nn−2\frac{n}{n-2}n−2n​

So the correct option is A.

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