Question

calculate the work done on an adiabatic change of an ideal gas from the state p¹v¹t¹ to state p²v²t²​

Answer 1

Answer:

Given:

Ideal gas changes within the given states through an Adiabatic Process.

To find:

Work done in this process :

Calculation:

1st method:

A general form of adiabatic process is as follows

$\boxed{P {V}^{ \gamma} = constant = c}$

$= > P = \dfrac{c}{ {V}^{ \gamma} }$

Now work done be dW

$\int \: dW = \int \: P \: dV$

$= > W = \int \: \dfrac{c}{ {V}^{ \gamma} } dV$

$= > W = c \int \dfrac{dV}{ {V}^{ \gamma} }$

$= > W = c \int {V}^{ - \gamma} dV$

$= > W = c( \dfrac{ {V}^{ - \gamma + 1} }{ - \gamma + 1} )$

Putting the limits :

$= > W = c( \dfrac{ {V_{2}}^{1 - \gamma} - {V_{1}}^{1 - \gamma} }{1 - \gamma} )$

2nd method:

Since heat transferred is zero , the work done is equal to the magnitude of internal energy change. This is based on 1st Law of Thermodynamics.

$w = - dU = (\dfrac{nRT_{1} - nRT_{2}}{ \gamma - 1} )$

Answer 2

Check the attachment....♡ :)