The internal energy of monoatomic ideal gas is 1.5 nRT. One mole of helium is kept in cylinder of cross section `8.5cm^2`. The cylinder is closed by a light frictionless piston. The gas is heated slowly in a process during which a total of 42 J heat is given to the gas. If the temperature rises through `2^@C` find the distance moved by the piston. Atmospheric pressure`=100kPa`

Explanation

given `n=1`,`A=85xx10^-4m^2`,`DeltaQ=42J`,` DeltaT=2^@C`
Atmospheric pressure `P_0=100Pa=10^5(N)/(m^2)`,`U=1.5nRT`
The gas is heated slowly i.e., pressure remains constant
`DeltaW=DeltaQ-DeltaU=42-1.5xx1xx8.3xx2=17.1J`
`P_0DeltaV=P_0Ax=DeltaW`
`10^5xx8.5xx10^-4x=17.1`
`x=0.2m=20m`
x distance moved by piston.