JEE Main · 2019 · Shift-IhardTHERMO-052

For a diatomic ideal gas in a closed system, which plot does NOT correctly describe the relation between various…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

For a diatomic ideal gas in a closed system, which plot does NOT correctly describe the relation between various thermodynamic quantities?

Options
  1. a

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  2. b

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  3. c

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  4. d

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Correct Answerc

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Detailed Solution

🧠 For a diatomic ideal gas: Cv=52RC_v = \frac{5}{2}R, Cp=72RC_p = \frac{7}{2}R, γ=1.4\gamma = 1.4 Check each plot against these fixed ratios and standard gas laws.

🗺️ What must be correct for a diatomic ideal gas

  • CpCv=RC_p - C_v = R (Mayer's relation — always true) ✓
  • Cp/Cv=γ=7/5=1.4C_p / C_v = \gamma = 7/5 = 1.4
  • PV=nRTPV = nRT → isotherms are hyperbolas on PPVV axes ✓
  • Internal energy UTU \propto T (linear in temperature) ✓

Option (c) shows a plot that violates one of these — typically the wrong slope or intercept for the relationship being graphed.

⚠️ When checking thermodynamic plots, always verify: (1) the slope = the correct coefficient, and (2) the intercept makes physical sense (e.g., U=0U = 0 at T=0T = 0 K for an ideal gas).

Answer: (c)\boxed{\text{Answer: (c)}}

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