1. Tardigrade
  2. Question
  3. Physics
  4. In an adiabatic changes the pressure and temperature of a monoatomic gas are related with relation P propto T C where C is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. In an adiabatic changes the pressure and temperature of a monoatomic gas are related with relation $P \propto T ^{ C }$ where $C$ is equal to

Thermodynamics

Solution:

Adiabatic process $P ^{1- \gamma} T ^{\gamma}= K$
general equation $P \propto T^{-\gamma / 1-\gamma}$
given equation $P \rightarrow T^{c}$
$\frac{-\gamma}{1-\gamma}= C$
$C=\frac{-\frac{5}{3}}{1-\frac{5}{3}}=\frac{\frac{-5}{3}}{\frac{-2}{3}} $
$\gamma$ for monoatomic $=\frac{5}{3}$
$C=\frac{5}{2}$