Question

Which of the following is true in the case of an adiabatic process, where $\gamma =C_p/C_V$?

• A. $p^{1-\gamma }{T}^{\gamma }=$ constant
• B. $p^{\gamma }{T}^{1-\gamma }=$ constant
• C. $p{T}^{\gamma }=$ constant
• D. $p^{\gamma }T=$ constant

Answer 1

The correct option is A $p^{1-\gamma }{T}^{\gamma }=$ constant

Adiabatic process : $P{V}^{\gamma }=constant$ .......(1)

Using ideal gas equation in (1), $V=\frac{nRT}{P}$

We get: $P\times (\frac{nRT}{P}{)}^{\gamma }=constant$

$⟹$ $P^{1-\gamma }{T}^{\gamma }=constant$