wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Which of the following is true in case of reversible adiabatic expansion?


A

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B


Adiabatic Expansion or Compression Process

As we know, in adiabatic process, heat change is zero.

q = 0 [No heat is allowed to enter or leave the system]

Now, as we know

ΔV = q + ω

ΔV = ω[q = 0]

If ω = ve ΔV = ve [by the system]

If ω = +ve ΔV = +ve[on the system]

Now, Let's try to find out the work done in adiabatic expansion.

As we know that,

Cv=(dVdT)v

dV = Cv . dT

and for finite change ΔV = CvΔT

Therefore, ω = ΔV = CvΔT

Here, the value of ΔT depends on the process whether it is reversible or irreversible.

Reversible Adiabatic Expansion

We know that,

ω = PΔV

& ω = CvΔT (as we just saw)

CvΔV = PΔV

For very small change in reversible process,

CvΔT = PdV

CvΔT = RTvdv(for one mole of gas) (As we know, Pv = nRT)

Cv.dTT = R.dVV

Integrating from T1 to T2 and V1 to V2

CvT2T1 dTT = Rv2v1 dvv

Cv logeT2T1 = R logev2v1 = Rlogev1v2

logT2T1 = Rcvlogv2v1 = Rcvlogv1v2

Now, as we know

Cp Cv = R

cpcv 1 = Rcv

(γ 1) = Rcv [ cpcv = γ]

Now, put value of RCv in eq. (4),

Log T2T1 = (γ 1)logv1v2

= log (v1v2) ...............(5)

or T2T1 = (v1v2)γ 1 .............(6)

T1T2 = (v2v1)γ 1 .............(7)

P1V1P2V2 =(v2v1)γ1 P2P1 = (v2v1)γ

P1vγ1 = P2vγ2

Pvγ = constant

Now, we know that

V1V2 = P2T1P1T2................(8)

Substituting (8) in (4)

(P2T1P1T2)γ 1 = T2T1

(P2P1)γ 1 = (T2T1)γ

(T1T2)γ = (P1P2)1 γ


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
First Law of Thermodynamics
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon