Which of the following relation is correct regarding one mole of an ideal gas for adiabatic reversible process?

Question

Which of the following relation is correct regarding one mole of an ideal gas for adiabatic reversible process? (A) ln(T2/T1)=(R/CV)ln(V2/V1) (B) ln(T2/T1)=(R/CP)ln(P1/P2) (C) ln(T2/T1)=(R/CP)ln(P2/P1) (D) (R/CV)ln(V1/ V2)=(R/CP)ln(P1/P2)

Tardigrade Admin · Accepted Answer

For adiabatic process (T2/ T1)=((V1/ V2))&gamma; - 1=((P1/P2))(1 - &gamma; /&gamma; ) ⇒ (T2/ T1)=((V1/ V2))(R/Cv)=((P2/P1))(R/CP) or ln(T2/ T1)=(R/Cv)ln(V1/ V2)=(R/CP)ln(P2/P1)

Q. Which of the following relation is correct regarding one mole of an ideal gas for adiabatic reversible process?

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{V}} l n \frac{V _{2}}{V _{1}}$

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{P}} l n \frac{P _{1}}{P _{2}}$

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{P}} l n \frac{P _{2}}{P _{1}}$

$\frac{R}{C _{V}} l n \frac{V _{1}}{V _{2}} = \frac{R}{C _{P}} l n \frac{P _{1}}{P _{2}}$

Q. Which of the following relation is correct regarding one mole of an ideal gas for adiabatic reversible process?

lnT1​T2​​=CV​R​lnV1​V2​​

lnT1​T2​​=CP​R​lnP2​P1​​

lnT1​T2​​=CP​R​lnP1​P2​​

CV​R​lnV2​V1​​=CP​R​lnP2​P1​​

For adiabatic process T1​T2​​=(V2​V1​​)γ−1=(P2​P1​​)γ1−γ​ ⇒T1​T2​​=(V2​V1​​)Cv​R​=(P1​P2​​)CP​R​ or lnT1​T2​​=Cv​R​lnV2​V1​​=CP​R​lnP1​P2​​

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{V}} l n \frac{V _{2}}{V _{1}}$

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{P}} l n \frac{P _{1}}{P _{2}}$

$l n \frac{T _{2}}{T _{1}} = \frac{R}{C _{P}} l n \frac{P _{2}}{P _{1}}$

$\frac{R}{C _{V}} l n \frac{V _{1}}{V _{2}} = \frac{R}{C _{P}} l n \frac{P _{1}}{P _{2}}$