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Calculate the work done in the following...

Calculate the work done in the following processes, when gas expands from `V_0` to `2V_0`
(a) `P=kV`, k is constant
(b) `T=T_0+alphaV`,`T_0`,`alpha:` constant n: number of moles of gas

Text Solution

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In case of variable quantities, work done can be calculated.
`W=int_(V1)^(V2)PdV`
(a) `W=int_(V0)^(2V0)kVdV=k|(V^2)/(2)|_(V0)^(2V0)`
`=(k)/(2)[(2V_0)^2-V_0^2]`
`=(3kV_(0)^(2))/(2)`
(b) `T=T_0+alphaV`
`(PV)/(nR)=T_0+alphaV`
`P=(nRT_0)/(V)+alphanR`
`W=int_(V0)^(2V0)PdV=int_(V0)^(2V0)((nRT_0)/(V)+alphanR)dV`
`=nRT_0|lnV|_(v0)^(2v0)+alphanR|V|_(V0)^(2v0)`
`nRT_0(ln2v_0-1nV_0)+alphanR(2V_0-V_0)`
`nRT_0ln(2)+alphanRV_0`
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