Question

prove that the isothermal elasticity of a gas is equal to its pressure .

Answer 1

For isothermal process
PV = K ................(1) [ T = Constant ]
differentiating equation (1) [ K = nRT = Constant ]
Pdv + vdp = 0
$$\begin{gathered} \mathbf{\Rightarrow }\mathbf{}\mathit{P}\mathit{d}\mathit{v}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{}\mathit{v}\mathbf{}\mathit{d}\mathit{p}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{P}\mathbf{=}\mathbf{}\frac{\mathbf{-}\mathbf{v}\mathbf{d}\mathbf{p}}{\mathbf{d}\mathbf{v}} \\ \mathbf{}\mathbf{}\mathbf{}\mathit{P}\mathbf{=}\mathbf{}\mathbf{-}\mathit{B}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{[}\mathbf{}\mathit{B}\mathbf{}\mathbf{-}\mathit{B}\mathit{u}\mathit{l}\mathit{k}\mathbf{}\mathit{m}\mathit{o}\mathit{d}\mathit{u}\mathit{l}\mathit{u}\mathit{s}\mathbf{}\mathbf{]}\mathbf{} \\ Henceisothermalelasticityisequaltopressure. \end{gathered}$$