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n moles of a monoatomic gas initiall at temp t is enclosed in a cylindrical vessel fitted with a light piston. Surrounding air temp =Ts=5T and atmos pressure=P. Heat may be conducted btw the surrounding & the gas through the bottom of the cylinder. The bottom has a surface area A,thickness t & thermal conductivity K. Assuming all changes to be slow find
1. rate of inc of internal energyof gas when temp of gas become 3T
2. the temp of gas changes from T to 2T in time t1 & 2T to 3T in t2 find t2-t1
i cant feel the Q pls give the fundas
i think light piston means isobaric system tell me if i m correct
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3 Answers
9yes ur right its isobaric cos itll adjust itself to atm P
1. U = Q- W
dU/dt = dQ/dt - dW/dt
use dQ/dt = kA/t ΔT dW/dt = nRdT/dt U =3/2 nRT →dU/dt =(3/2)nRdT/dt
ull get (3/5)dQ/dt as ans =6kA/5t
2. similarly use abv eq to get
5/2 nRdT/dt = kA/t ΔT integrate and solve to get 5nR/2kA ln9/8