Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)*V(initial)- P(final)*V(final)]/(gamma-1), using integration [integral of PdV]

Question

Aman Bansal · Answer

Dear Arnab,

In an adiabatic quasi-static process we can write the formula

PV^Y = constant

constant = K for simplification

Since its adiabatic no heat change so Q=0

Using the first law of thermo

Q= ΔU -W

We know that W = -PdV
and P= K/V^Y

so...
W = ΔU
W = -PdV
W = -(K/V^Y)*dV
W = -K∫(1/V^Y)*dV
W = -K[V^(1-Y)/(1-Y)]*∫dV
W = -(K/(1-Y))[Vf^(1-Y) - Vi^(1-Y)]
W = -(K/(1-Y))[Vf^(-Y)*Vf - Vi^(-Y)*Vi]
W = -(1/(1-Y))[((Vf*K)/(Vf^Y)) - ((Vi*K)/(Vi^Y))]

since Pi = K/Vi^Y and Pf = K/Vf^Y sub those in

W = -(1/(1-Y))(Vf*Pf - Vi*Pi)
Times this by (-1/-1)

and we get

W = (PfVf - PiVi)/(Y-1)

This is where I get to not sure where to go from here to make this into

W= (PfVf)/(Y-1)[1 - (Pi/Pf)^((Y-1)/Y)]

Best Of Luck...!!!!

Cracking IIT just got more exciting,It’s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)V(initial)- P(final)V(final)]/(gamma-1), using integration [integral of PdV]

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)V(initial)- P(final)V(final)]/(gamma-1), using integration [integral of PdV]

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Thermal Physics

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)*V(initial)- P(final)*V(final)]/(gamma-1), using integration [integral of PdV]

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)*V(initial)- P(final)*V(final)]/(gamma-1), using integration [integral of PdV]

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Thermal Physics

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)V(initial)- P(final)V(final)]/(gamma-1), using integration [integral of PdV]

Prove that work done by an ideal gas in an adiabatic process is W =[P(initial)V(initial)- P(final)V(final)]/(gamma-1), using integration [integral of PdV]