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 ineach cylinder. If the rise in temperature of the gas in A to 30 K, then the rise in temperature of the gas in B is

Two cylinders A and B fitted with pistons contain equal amounts of an

1.	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 ineach cylinder. If the rise in temperature of the gas in A to 30 K, then the rise in temperature of the gas in B is
Answer» <P>30 K 18 K 50 K 42 K Solution :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 the gas in A is `Delta Q_(A) = nC_(P)Delta T_(A)` and that given to the gas in B is `Delta Q_(B) - nC_(V)delta T_(B)` Since `Delta Q_(A) = Delta Q_(B) :. nC_(P)Delta T_(A) = nC_(V)Delta T_(B)` or `Delta T_(B) = (C_(P))/(C_(V)) Delta T_(A) = (7)/(5) xx 30 K = 42 K`(`because` for a diatomic gas , `C_(V)//C_(P) = 5//7`)