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In a certain thermodynamical process, th...

In a certain thermodynamical process, the pressure of a gas depends on its volume as `kV^(3)`. The work done when the temperature changes from `100^(@)`C to `300^(@)C` will be x times nR, where n denotes number of moles of a gas. Find x.

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The correct Answer is:
50
`P=kV^3`
`T_i = 100^@C and T_f = 300^@C`
`DeltaT = 300-100`
`DeltaT = 200^@C`
`P=kV^3`
Now, PV = nRT
`:. kV^4 = nRT`
Now, `4kV^3` dV = nRdT
`:.` PdV = nRdT/4
`:.` Work `=intPdV=int(nRdT)/4=(nR)/4DeltaT`
`=200/4 xxnR =50nR`
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