Derive the mathematical expression for first law of thermodynamics

Asked by admin @ 20/08/2021 in Physics viewed by 340 People

Derive first law of thermodynamics mathematically

Answered by admin @ 20/08/2021

$\pink{ \sf \underline{ \underline{ \large{ \: First \: law \: of \: thermodynamics \: \: }}}}$

First law of thermodynamics states that energy can neither be created nor be destroyed

The mathmetical formulation of first law of thermodynamics : Δ U = q + w

Where ,

$\star$ Δ U = change is internal energy

$\star$ q = heat

$\star$ w = work done

Now , we are going to derive this equation or formula

Suppose ,

The initial internal energy of the system = U1

if it gain or absorbs heat q its internal energy will become

U1 + q

If further work w is done on the system , the internal energy will further increases and become

U1 + q + w

Consider , this final energy as U2

Then ,

$\sf \implies U2 = U1 + q + w \\ \\ \sf \implies U2 - U1 = q + w \\ \\ \sf \implies \red{\fbox{Δ U = q + w}}$

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