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

Calculate the work done in the following processes, when gas expands f

1.	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
Answer» 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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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

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