A vertical cylinder-piston system holds a sample of monatomic gas. The piston has an area of 0.02 m2 and a mass of 20 kg. Calculate the amount of heat that should be transferred to the gas, to lift the pis- ton by 10 cm. Atmospheric pressure is 100 kPa.
Consider a vertical cylinder-piston system that holds a sample of a monoatomic gas having a heat capacity,(Cv)at a constant volume of a gas.
Cylinder-piston has an area,(A) in meter2 and a mass of (M) in a kilogram.
A=0.02 m2-------------(1)
M=20 Kg--------------(2)
Cv=----(3) [Here, R is ideal gas constant]
Now, let U be the internal energy of the system.
Then, U =Cv x T ----(4) [ T is the change in temperature]
Putting the value of Cv from (3) in (4) we get,
U = x T
U = x V ----(5) [Using ideal gas equation]
Let the amount of heat be (Q) in Joule that should be transferred to the gas, to lift the piston by (l) in the meter.
l=10 cm =0.1 m ------(6) [Using 100 cm =1m]
V=A x l-----------(7) [Volume of the cyclinder]
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