If C for an ideal gas is given by CV = (3 + 2T)R, Where T is... | PHYSICS - THERMODYNAMIC PROCESSES | SolveeIt | Solveeit

Today, August 24

Question

If C for an ideal gas is given by C_V = (3 + 2T)R, Where T is absolute temperature of gas, then the equation of adiabatic process for this gas is :

A

VT² = constant

B

VT³e^–2T = C

C

VT²e^2T = constant

D

VT³e^2T = constant

Answer

VT³e^2T = constant

Explanation

Solution

C_V = (3 + 2T)R

dQ = dU + PdV

adiabatic process dQ = 0

0 = Rn (3 + 2T)dT + PdV

0 = Rn(3 + 2T)dT + dV=

– logV = 3logT + 2T + C

– logV – logT³ = 2T + C

logVT³ = – 2T – C

logVT³ = – 2T

VT³ = e^–2T = C

VT³ e^2T = C