1800-150-456-789
FlagBACK
Flag Thermal Physics> thermoprob4...
question mark

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]

Arnab Mandal , 13 Years ago
Grade 11
anser 1 Answers
Aman Bansal

Last Activity: 13 Years ago

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

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

Other Related Questions on Thermal Physics

question mark
A container filled with a sample of an Idea gas at the pressure of 1.5atm. the gas is compressed isothermal ly to one fourth of its original volume. What is the new pressure of the gas?
Thermal Physics
0 Answer Available

Last Activity: 1 Year ago(s)

question mark
how do we know the electric field due to an electric dipole of dipole moment P at distance r from the centre of dipole is fiven by .. where theta is angle between p amd r vector..
Thermal Physics
0 Answer Available

Last Activity: 2 Year ago(s)

question mark
A A mole of helium gas initially at stp undergoes an isovolumetric process in which its pressure falls to half its initial value. The work done by gas is
Thermal Physics
0 Answer Available

Last Activity: 2 Year ago(s)

question mark
\t5000 J of heat are added to two moles of an ideal monatomic gas, initially at a temperature of 500 K, while the gas performs 7500 J of work. What is the final temperature of the gas? step by step please
Thermal Physics
1 Answer Available

Last Activity: 2 Year ago(s)

question mark
Please help me with theanswer of this questionrelated to radiation graph
Thermal Physics
0 Answer Available

Last Activity: 2 Year ago(s)