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

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 (A) (3/2) (B) (5/2) (C) (7/9) (D) (9/7)

Tardigrade Admin · Accepted Answer

Adiabatic process P 1- &gamma; T &gamma;= K general equation P propto T-&gamma; / 1-&gamma; given equation P arrow Tc (-&gamma;/1-&gamma;)= C C=(-(5/3)/1-(5)3)=((-5/3)/(-2)3) &gamma; for monoatomic =(5/3) C=(5/2)

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

$\frac{3}{2}$

$\frac{5}{2}$

$\frac{7}{9}$

$\frac{9}{7}$

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

Q. In an adiabatic changes the pressure and temperature of a monoatomic gas are related with relation P∝TC where C is equal to

23​

25​

97​

79​

Adiabatic process P1−γTγ=K general equation P∝T−γ/1−γ given equation P→Tc 1−γ−γ​=C C=1−35​−35​​=3−2​3−5​​ γ for monoatomic =35​ C=25​