Question

write mathematical form of first law of thermodynamics. use the equation to prove q_(p)​ = delta H

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{first}\mathrm{law}\mathrm{of}\mathrm{thermodynamics}, \\ \mathrm{q}=∆\mathrm{U}+\mathrm{w} \\ \mathrm{and}\mathrm{w}=\mathrm{P}∆\mathrm{V} \\ \mathrm{Therefore},\mathrm{q}=∆\mathrm{U}+\mathrm{P}∆\mathrm{V} \\ \mathrm{At}\mathrm{constant}\mathrm{pressure}, \\ {\mathrm{q}}_{\mathrm{p}}=∆\mathrm{U}+\mathrm{P}∆\mathrm{V}...\left(\mathrm{i}\right) \\ \mathrm{Now},\mathrm{we}\mathrm{know}\mathrm{that} \\ ∆\mathrm{H}=∆\mathrm{U}+\mathrm{P}∆\mathrm{V}...\left(\mathrm{ii}\right) \\ \mathrm{Comparing}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get} \\ {\mathrm{q}}_{\mathrm{P}}=∆\mathrm{H} \end{gathered}$$