Two cylinders A and B fitted with pistons con | vedclass

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Question

(D) In both cylinders $A$ and $B$,the gases are diatomic $(\gamma = 1.4)$.For cylinder $A$,the piston is free to move,which implies an isobaric proces

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(D) In both cylinders $A$ and $B$,the gases are diatomic $(\gamma = 1.4)$.For cylinder $A$,the piston is free to move,which implies an isobaric process. The heat supplied is given by $(\Delta Q)_A = \mu C_P (\Delta T)_A$.For cylinder $B$,the piston is fixed,which implies an isochoric process. The heat supplied is given by $(\Delta Q)_B = \mu C_V (\Delta T)_B$.Since the same amount of heat is given to both,$(\Delta Q)_A = (\Delta Q)_B$.Therefore,$\mu C_P (\Delta T)_A = \mu C_V (\Delta T)_B$.Rearranging for $(\Delta T)_B$,we get $(\Delta T)_B = \frac{C_P}{C_V} (\Delta T)_A = \gamma (\Delta T)_A$.Given $\gamma = 1.4$ and $(\Delta T)_A = 30\,K$,we have $(\Delta T)_B = 1.4 	imes 30 = 42\,K$.

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