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An ideal monoatomic gas is confined by a...

An ideal monoatomic gas is confined by a spring loaded massless piston of cross-section `8.0xx10^-3m^2`. Initially, the gas is at 300K and occupies a volume of `2.4xx10^-3m^3` and the spring is in its relaxed state. The gas is heated by an electric heater until the piston moves out slowly without friction by 0.1 m. Calculate
(a) the final temperature of the gas and
(b) the heat supplied by the heater.
The force constant of the spring is `8000N//m`, atmospheric pressure `1.0xx10^5N//m^2`. The cylinder and the piston are thermally insulated.

Text Solution

Verified by Experts

The correct Answer is:
`800K , 720K`
Final volume of chamber = `V_(0) + Ax = 3.2 xx 10^(-3)m^(3)`
Final pressure in chamber = `P_(0) + (kx)/(A) = 2xx 10^(5)N//m^(2)`
From ideal gas equation `(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`
`T_(2) = (P_(2)V_(2))((T_(1))/(P_(1)V_(1))) = 800K`
Work done by gas =`underset(0)overset(0.1)int(P_(0) + (Kx)/(A))Adx=120J`
Change in internal energy `DeltaU =nC_(V)DeltaT`
`implies DeltaU = ((P_(1)V_(1))/(RT_(1)))((3)/(2)R) DeltaT=600J`
`therefore` Heat Supplied = `120+600= 720J`
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