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  • Which of the following is equation of state for an adiabatic process?Option: 1 <img alt="\mathrm{p V^\gamma=\text { constant }}" src="/latex-image/?%

Which of the following is equation of state for an adiabatic process?

Option: 1

\mathrm{p V^\gamma=\text { constant }}


Option: 2

\mathrm{p / \rho^\gamma=\text { constant }}


Option: 3

\mathrm{T V^{\gamma-1=} \text { constant }}


Option: 4

All of the above


Answers (1)

best_answer

In an adiabatic process,

\mathrm{\begin{aligned} & p V^\gamma=\text { constant } \\ & \text { As } V \propto \frac{1}{\rho} \\ & \therefore \frac{p}{\rho^\gamma}=\text { constant } \end{aligned}}

\mathrm{\text { As } p=\frac{R T}{V} \text {, }}

\mathrm{\therefore\left(\frac{R T}{V}\right) \times V^\gamma=\text { constant or } T V^{\gamma-1}=\text { constant }}

\mathrm{\text { As } \quad V=\frac{R T}{p} \text {, }}

\mathrm{\therefore p\left(\frac{R T}{p}\right)^\gamma=\text { constant or } \frac{T^\gamma}{p^{\gamma-1}}=\text { constant }}

All the choices are correct

Posted by

Ajit Kumar Dubey

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