ThermodynamicsEasy
Question
Two cylinders A and B fitted with piston contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in the temperature of the gas in B is
Options
A.30 K
B.18 K
C.50 K
D.42 K
Solution
A is free to move, therefore, heat will be supplied at constant pressure
∴ dQA = nCp dTA .......(i)
B is held fixed, therefore, heat will be supplied at constant volume
∴ dQB = nCv dTB .......(ii)
But dQA dQB [Given]
∴ nCp dTA = nCv dTB ∴ dTB =
dTA
= γ(dTA) [γ = 1.4(diatomic)]
(dTA = 30 K)
= (1.4) (30 K)
∴ dTB = 42K.
∴ dQA = nCp dTA .......(i)
B is held fixed, therefore, heat will be supplied at constant volume
∴ dQB = nCv dTB .......(ii)
But dQA dQB [Given]
∴ nCp dTA = nCv dTB ∴ dTB =
dTA = γ(dTA) [γ = 1.4(diatomic)]
(dTA = 30 K)
= (1.4) (30 K)
∴ dTB = 42K.
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