For an adiabatic process, the relation between V and T is given by

Question

For an adiabatic process, the relation between V and T is given by (A)  TV&gamma; = constant (B)  T&gamma; V = constant (C)  TV1-&gamma; = constant (D)  TV&gamma; -1 = constant

Tardigrade Admin · Accepted Answer

In an adiabatic process PV&gamma; = textconstant Using ideal gas equation, PV = RT ∴ ( (RT/V) )V&gamma; = textconstant or TV&gamma; -1= textconstant (as R is a gas constant)

Q. For an adiabatic process, the relation between V and T is given by

$T V^{γ}$ = constant

$T^{γ} V$ = constant

$T V^{1 - γ}$ = constant

$T V^{γ - 1}$ = constant

In an adiabatic process $P V^{γ} = constant$ Using ideal gas equation, PV = RT $∴$ $(\frac{RT}{V}) V^{γ} = constant$ or $T V^{γ - 1} = constant$ (as R is a gas constant)

Q. For an adiabatic process, the relation between V and T is given by

TVγ = constant

TγV = constant

TV1−γ = constant

TVγ−1 = constant

In an adiabatic process PVγ=constant Using ideal gas equation, PV = RT ∴ (VRT​)Vγ=constant or TVγ−1=constant (as R is a gas constant)

$T V^{γ}$ = constant

$T^{γ} V$ = constant

$T V^{1 - γ}$ = constant

$T V^{γ - 1}$ = constant

In an adiabatic process $P V^{γ} = constant$ Using ideal gas equation, PV = RT $∴$ $(\frac{RT}{V}) V^{γ} = constant$ or $T V^{γ - 1} = constant$ (as R is a gas constant)