In a certain thermodynamical process, the pressure of a gas depends...

$P = k{V}^{3}$

${T}_{i} = 100 ° C \text{ and } {T}_{f} = 300 ° C$

$\DeltaT = 300 - 100$

$\DeltaT = 200 ° C$

$P = k{V}^{3}$

now $PV = nRT$

$∴ k{V}^{4} = nRT$

now $4k{V}^{3}dV = nRdT$

$∴ PdV = nRdT / 4$

$∴$ Work $= ∫ PdV = ∫ \dfrac{nRdT}{4} = \dfrac{nR}{4}\DeltaT$

$= \dfrac{200}{4} \times nR = 50nR$