Question

A cylinder fitted with a piston contains an ideal monatomic gas at any temperature of 400 kelvin

Answer 1

your question is incomplete. A complete question is -----> Two cylinders A and B fitted with pistons contain equal amount 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


solve :- a/c to question, 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.
so, $Q_A=Q_B$

for cylinder A, pressure remains constant which for cylinder B, volume remains constant.

so, $Q_A=\textbf{heat at constant pressure}=nC_p\Delta T_A$

and $Q_B=\textbf{heat at constant volume}=nC_v\Delta T_B$

now, $nC_p\Delta T_A=nC_v\Delta T_B$

or, $\Delta T_B=\frac{C_p}{C_v}\Delta T_A$

or, $\Delta T_B=\frac{7}{5}\times30$

or, $\Delta T_B=42K$

hence, rise in temperature of the gas B is 42K.