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  • 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 t

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 30 K, then the rise in temperature of the gas in B is

Option: 1

30 K


Option: 2

18 K


Option: 3

50 K


Option: 4

42 k


Answers (1)

best_answer

Heat is given to the gas in cylinder A at constant pressure while the same amount of heat is given to the gas in cylinder B at constant volume. Heat given to gas in A is

\mathrm{Q_A=n C_p \Delta T_A}

\mathrm{\text { Heat given to gas in } B \text { is } Q_B=n C_v \Delta T_B}

\mathrm{\text { Since } Q_A=Q_B \text {, we have }}

\mathrm{\begin{aligned} & n C_p \Delta T_A=n C_v \Delta T_B \\ & \text { Or } \Delta T_B=\frac{C_p}{C_v} \Delta T_A=\frac{7}{5} \times 30 \mathrm{~K}=42 \mathrm{~K} \end{aligned}}

\mathrm{\text { ( } \because \text { for a diatomic gas, } C_p / C_v=7 / 5 \text { ) }}

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