Which of the following is true in the case of an adiabatic process, where γ = Cp / Cv ?

Question

Which of the following is true in the case of an adiabatic process, where &gamma; = Cp / Cv ? (A) p1 -&gamma; T1 - y = constant (B) p&gamma; T1 - &gamma; = constant (C) p T y = constant (D) p&gamma; T = constant

Tardigrade Admin · Accepted Answer

For adiabatic change equation of state is pV&gamma; = constant It can also be re-written as TV&gamma; - 1 = constant as p = ( n RT/V) and p1- &gamma; Ty = constant as V = (nRT/p)

Q. Which of the following is true in the case of an adiabatic process, where $γ = C_{p} / C_{v}$ ?

$p^{1 - γ} T^{1 - y}$ = constant

$p^{γ} T^{1 - γ}$ = constant

$p T^{y}$ = constant

$p^{γ} T$ = constant

For adiabatic change equation of state is
$p V^{γ}$ = constant
It can also be re-written as
$T V^{γ - 1}$ = constant as $p = \frac{n RT}{V}$
and $p^{1 - γ} T^{y}$ = constant as $V = \frac{n RT}{p}$

Q. Which of the following is true in the case of an adiabatic process, where γ=Cp​/Cv​ ?

p1−γT1−y = constant

pγT1−γ = constant

pTy = constant

pγT = constant