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

Answer

`20 cm`

Explanation

Here, `dU= 1.5 n R DeltaT=1.5xx1xx8.3xx2= 24.9J`
`dQ= 42J`
According to first law of thermodynamics,
`dU+dW=dQ`
`dW=dQ-dU= 42-24.9= 17.1J`
As `dW= PA.dx`
`:. dx=(dW)/(PA)=(17.1)/(10^(5)xx(8.5xx10^(-4)))m`
`dx=(17.1xx100)/(85)=20 cm`