Question

Obtain an expression for work done, change in internal energy and heat supplied in an isobaric [3] process for a gas.

Answer 1

To find:

An expression for work done, change in internal energy and heat supplied in an isobaric [3] process for a gas.

Solution:

Isobaric process refers to a thermodynamic process associated with constant external pressure.

Let us assume the following:

• Internal energy change : ∆U
• Heat change : ∆Q
• Work : W
• Number of moles : $\mu$

In all thermodynamic process , ∆U is given as :

$\boxed{ \rm \therefore \: \Delta U = \mu C_{v}\Delta \theta \: \: \: \: \: ........(1)}$

In constant pressure , the heat change is:

$\boxed{ \rm \therefore \: \Delta Q = \mu C_{p}\Delta \theta \: \: \: \: \: ........(2)}$

According to 1st Law of thermodynamics:

$\rm \therefore \: \Delta Q =\Delta U + W$

$\rm \implies \: \mu C_{p}\Delta \theta =\mu C_{v}\Delta \theta + W$

$\boxed{ \rm \implies \: W = \mu (C_{v} - C_{p})\Delta \theta}$

In other words , it can also represented as:

$\boxed{ \rm \implies \: W =P\Delta V }$

Hope It Helps.

Answer 2

Answer:

Consider n moles of a gas enclosed in a cylinder fitted with a movable, massless and

frictionless piston. We assume that the gas behaves as an ideal gas so that we can use

the equation of state PV  nRT.

P

P A

Isobar

B

Vi Vf

V

P–V diagram for an isobaric process

Consider an isobaric expansion (or compression) of the gas in which the volume of

the gas changes from Vi

to Vf

and the temperature of the gas changes from Ti

to Tf

when the pressure (P) of the gas is kept constant. The work done by the gas,

W 

Vf

Vi

PdV  P 

Vf

Vi

dVP (Vf

  Vi

) ... (1)

Now, PVinRTi

and PVfnRTf

 PVf

  PVinRTf

  nRTi

 P (Vf

  Vi

)nR (Tf

  Ti

)

 From Eq. (1), WnR (Tf

  Ti

)The change in the internal energy of the gas,

*UnCV (Tf

  Ti

) ... (3)

where CV is the molar specific heat of the gas at constant volume.

From Eqs. (2) and (3), we have, the heat supplied to the gas,

Q*UW nCV (Tf

  Ti

)nR (Tf

  Ti

)

n(CVR)(Tf

  Ti

)

 QnCP (Tf

  Ti

) ... (4)

where CP (CVR) is the molar specific heat of the gas at constant pressure.