For an isobaric process, the ratio of Δ Q (amount of heat supplied) to the Δ W (work done by the gas) is (γ=(CP/CV))

Question

For an isobaric process, the ratio of Δ Q (amount of heat supplied) to the Δ W (work done by the gas) is (&gamma;=(CP/CV)) (A) &gamma; (B) &gamma;-1 (C) (&gamma;/&gamma;+1) (D) (&gamma;/&gamma;-1)

Tardigrade Admin · Accepted Answer

For isobaric process Δ Q=n Cp Δ T and Δ W=n R Δ T So, (Δ Q/Δ W)=(CP/R)=(CP/CP-CV)=(1/1-(CV)CP)=(&gamma;/&gamma;-1) [∵ (cP/cv)=&gamma;]

Q. For an isobaric process, the ratio of $Δ Q$ (amount of heat supplied) to the $Δ W$ (work done by the gas) is $(γ = \frac{C _{P}}{C _{V}})$

$γ$

$γ - 1$

$\frac{γ}{γ + 1}$

$\frac{γ}{γ - 1}$

For isobaric process $Δ Q = n C_{p} Δ T$ and $Δ W = n R Δ T$
So, $\frac{Δ Q}{Δ W} = \frac{C _{P}}{R} = \frac{C _{P}}{C _{P} - C _{V}} = \frac{1}{1 - \frac{C _{V}}{C _{P}}} = \frac{γ}{γ - 1}$
$[∵ \frac{c _{P}}{c _{v}} = γ]$

Q. For an isobaric process, the ratio of ΔQ (amount of heat supplied) to the ΔW (work done by the gas) is (γ=CV​CP​​)

γ

γ−1

γ+1γ​

γ−1γ​

For isobaric process ΔQ=nCp​ΔT and ΔW=nRΔT So, ΔWΔQ​=RCP​​=CP​−CV​CP​​=1−CP​CV​​1​=γ−1γ​ [∵cv​cP​​=γ]

Q. For an isobaric process, the ratio of $Δ Q$ (amount of heat supplied) to the $Δ W$ (work done by the gas) is $(γ = \frac{C _{P}}{C _{V}})$

$γ$

$γ - 1$

$\frac{γ}{γ + 1}$

$\frac{γ}{γ - 1}$

For isobaric process $Δ Q = n C_{p} Δ T$ and $Δ W = n R Δ T$
So, $\frac{Δ Q}{Δ W} = \frac{C _{P}}{R} = \frac{C _{P}}{C _{P} - C _{V}} = \frac{1}{1 - \frac{C _{V}}{C _{P}}} = \frac{γ}{γ - 1}$
$[∵ \frac{c _{P}}{c _{v}} = γ]$