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Heat and Thermodynamics question

2023 · 31 Jan · Shift 1 · Q63
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  5. /2023 · 31 Jan · Shift 1 · Q63

Heat and Thermodynamics question

2023 · 31 Jan · Shift 1 · Q63

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
The correct relation between γ=cpcv\gamma = {{{c_p}} \over {{c_v}}}γ=cv​cp​​ and temperature T is :
  1. A
    γ∝T\gamma \propto Tγ∝T
  2. B
    γ∝1T\gamma \propto {1 \over {\sqrt T }}γ∝T​1​
  3. C
    γ∝1T\gamma \propto {1 \over T}γ∝T1​
  4. D
    γ∝T∘\gamma \propto T^\circγ∝T∘
View written solutionFree

Correct answer: D

  1. We need the relation between γ=cpcv\gamma = \frac{c_p}{c_v}γ=cv​cp​​ and temperature TTT.

  2. For an ideal gas, cp−cv=Rc_p - c_v = Rcp​−cv​=R where RRR is the gas constant.

  3. In standard thermodynamics for an ideal gas with fixed molecular structure (no change in degrees of freedom over the temperature range considered), both cpc_pcp​ and cvc_vcv​ are constants.

  4. Therefore their ratio γ=cpcv\gamma = \frac{c_p}{c_v}γ=cv​cp​​ is also constant, i.e. independent of temperature.

  5. Hence, γ∝T0\gamma \propto T^0γ∝T0 which means γ\gammaγ does not vary with TTT.

  6. Checking options:

  • A: γ∝T\gamma \propto Tγ∝T ❌
  • B: γ∝1T\gamma \propto \frac{1}{\sqrt{T}}γ∝T​1​ ❌
  • C: γ∝1T\gamma \propto \frac{1}{T}γ∝T1​ ❌
  • D: γ∝T0\gamma \propto T^0γ∝T0 ✅

Therefore, the correct option is D.

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