1. An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston if cross-section 
. Initially the gas is at 300 K and occupies a volume of 
and the spring is in a relaxed state. The gas is heated by a small heater coil H . The force constant of the spring is 8000 N / m , and the atmospheric pressure is 
. The cylinder and piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and cylinder. There is no heat loss through heater coil wire leads and thermal capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by 0.1 m , then the final temperature is
Text Solution
Verified by ExpertsB
, 
and T 1 = 300 K (given)
If area of cross-section of piston is A and it moves through distance x then increment in volume of the gas = Ax
and if force constant of a spring is k then force F = kx and pressure = 
and 
From ideal gas equation 
⇒ ⇒ 
⇒ ⇒ 
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