A vertical hollow cylinder contains an ideal gas. The gas is enclosed by a `5kg` movable piston with an area of cross-section `5 xx 10^(-3)m^(2)`. Now, the gas is heated slowly from `300K` to `350K` and the piston rises by `0.1m`. The piston is now clamped at this position and the gas is cooled back to `300K`. Find the difference between the heat energy added during heating process and energy lost during the cooling process. `("1atm pressure" = 10^(5)Nm^(-2)]`

Options

A. 65 J
B. 55 J
C. 75 J
D. 95 J

Answer

55 J

Explanation

`(DQ)_(P) = nC_(P) triangleT = triangleU + triangleW`
When the pistion is clamped, volume becomes constant
`therefore` Heat withdrawn,
`(triangleQ)_(v) = nC_(v) triangleT = triangleU`
or `(triangleQ)_(P)-(triangleQ)_(v) = triangleW= P triangle V `
`P=[P_(0)+(Mg)/(A)]`
`triangleV = A(0.1)`
`(triangleQ)_(p)-(triangleQ)_(v) =(P_(0)+(Mg)/(A)) A.(1)`
`=[10^(5)xx5xx10xx^(-3)+xx10](0.1)`