Figure shows a cylindrical container containing oxyegn `(gamma = 1.4)` and closed by a 50 kg frictionless piston. The area of cross section is `100cm(2)` , atmospheric pressure is `100 kPa`+E2 and g is 10 m s^(-2)`. The cylinder is slowly heated for some time. Find the amount of heat supplied to gas if the piston moves out through a distsnce of 20 cm.
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Explanation

`gamma =1.4`, Weight of piston (w) `= 50 kg`, Area of cross section of piston(A)
`=100 cm^2`
Atmospheric pressure `(P_0) = 100 kPa`,
`g=10 m//s^2, x=20 cm`,
`dW = Pdv= ((mg)/A+P_0).Adx`
`= ((50xx10)/(100xx10^(-4)) + 10^(5))`
`(100 xx 10 ^(-4) xx 20 xx 10^(-2))`
`= (5xx10^(4) xx10^(5) ) xx 20 xx 10^(-4)`
`= 1.5 xx 10^(5) xx 20 xx 10^(-4)`
`=300 J`.
Hence `nRdT = 300`ltbgt `dT= 300/nR` ltbgt So, `dQ=nCpdT=nc_p xx((300)/(nR))`
`=(ngammaR300)/((gamma-1)nR`
`= ((300xx1.4)/0.4)`
`=1050J`