An ideal monatomic gas is confined in a cylinder by a spring-loaded massless piston of cross-section 8 x 10 -3 m 2 . The piston can slide on the walls of the cylinder without any friction. Initially, the gas is at 300 K and occupies a volume of 2 .4 x 10 -3 m 3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N/rn and atmospheric pressure is 1 x 10 5 N/m 2 .
Text Solution
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T 2 = 800 K, Q = 720 J
In the initial condition
P 1 = 10 5 Pa, V 1 = 2. 4 x 10 -3 m 3 , T 1 = 300 K
Finally,
P 2 = P 1 + 
= 2 x 10 5 Pa
V 2 = V 1 + Ax = 3. 2 x 10 -3 m 3
, on solving we get
T 2 = 800 K
Applying work-energy theorem for the piston
W gas + W aimos + Spring = 0
W gas = P 0 Ax + 
kx 2 = 120 J
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