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 $$2013$$]

Question

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 $$2013$$]

Infinity Learn · Accepted Answer

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

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