An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure).Initially the gas is at temperature T 1 , pressure P 1 and volume V 1 and the spring is in its relaxed state. The gas is then heated very slowly to temperature T 2 , pressure P 2 and…

Question

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure).Initially the gas is at temperature $T_{1}$ , pressure $P_{1}$ and volume $V_{1}$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_{2}$ , pressure $P_{2}$ and volume $V_{2}$ . During this process the piston moves out by a distance $x$ . Ignoring the friction between the piston the cylinder, the correct statement(s) is (are)

Aicharya · Accepted Answer

(i) P = P 1 + K x A P 2 = 3 2 P 1 ⇒ x = V 1 A 3 P 1 2 = P 1 + K x A K x = P 1 A 2 Energy of spring 1 2 K x 2 = P 1 A 4 x = P 1 V 1 4 (ii) ∆ U = f 2 P 2 V 2 - P 2 V 1 = 3 P 1 V 1 (iii) P f = 4 P 1 3 K X = P 1 3 A X = 2 V 1 A W g a s = - W P a t m + W s p r i n g = P 1 A x + 1 2 K x . x = + P 1 A . 2 V 1 A + 1 2 . P 1 A 3 . 2 V 1 A = 2 P 1 V 1 + P 1 V 1 3 = 7 P 1 V 1 3 (iv) ∆ Q = W + ∆ U = 7 P 1 V 1 3 + 3 2 P 2 V 2 - P 1 V 1 = 7 P 1 V 1 3 + 3 2 4 3 P 1 . 3 V 1 - P 1 V 1 = 7 P 1 V 1 3 + 9 2 P 1 V 1 = 41 P 1 V 1 6

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the…

Solution