One mole of a monoatomic gas is enclosed in a cylinder and occupies a volume of `4` liter at a pressure `100N//m^(2)` . It is subjected to process `T = = alphaV^(2)`, where `alpha` is a positive constant , `V` is volume of the gas and `T` is kelvin temperature. Find the work done by gas (in joule) in increasing the volume of gas to six times initial volume .

Answer

7

Explanation

`W= intPdV ` where `P = (nRT)/(V) = alphanRV implies W = n alphaR underset(V_(0))overset(6V_(0))int VdV= (nalphaR)/(2)[(6V_(0))^(2) - (V_(0))^(2)]`
`implies W=(nalphaR)/(2) (35) V_(0)^(2) = (P_(0)V_(0) xx 35)/(2) (because alpha= (P_(0))/(nRV_(0)))`