Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. Piston A is free to move and piston of B is fixed. Same amount of heat is given to the gases in the two cylinders. Temperature of the gas in cylinder A increases by 30 K, then increase in temperature of the gas in the cylinder B is ( γ = 14 for diatomic gas) [EAMCET 2013]

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24 K

36 K

54 K

42 K

answer is D.

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Detailed Solution

We know that, dQ=nCpdTA=nCVdTB∵ nCpdTA=nCVdTB⇒ CpCV=dTBdTA⇒ γ=dTBdTA ∵γ=CpCV⇒ dTB=γdTA=1.4×30=42K

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