Atomic StructureHard

Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move while that of 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 30K, then the rise in temperature of the gas in B is :-

Options

A.30 K
B.18 K
C.50 K
D.42 K

Solution

In both cylinders A and B the gases are diatomic (γ = 1.4). Piston A is free to move i.e., it is isobaric process. Piston B is fixed i.e., it is isochoric process. If same amount of heat ᐃQ is given to both then
(ᐃQ)isobaric = (ᐃQ)isochoric ⇒ μCp(ᐃT)A = μCv(ᐃT)B
⇒ (ᐃT)B = (ᐃT)A = γ (ᐃT)A = 1.4 × 30 = 42 K

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