Heat transfer for different thermodynamic process:

In the thermodynamics it is very important to understand the phenomenon of heat transfer .

Heat is a boundary phenomenon and it is said to be transferred only when it crosses the boundary .

In detail we had discussed about heat transfer in previous post

Heat transfer for different thermodynamic processes :

(a) Isochoric process :

In Isochoric process volume remains constant.

i.e.,. V = constant

Therefore , dV = 0

And hence , ∆ W = 0

from first law of thermodynamics :

∆Q = dU + ∆W

As ∆W = 0

Therefore ,

∆Q = dU

and

dU = mc_v dT

and it is valid only for :

• Volume = constant, any gas

OR

• Ideal gas , any process

Note :

For Isochoric process, heat transfer is equal to the change in internal energy.

(b) Isobaric process :

In Isobaric process , pressure remains constant.

i.e., P = constant

therefore ,

∆W = P ( V₂ – V₁ )

and dU = U₂ – U₁

From first law of thermodynamics ,∆Q = dU + ∆W

∆Q = U₂-U₁ +P(V₂-V₁)

∆Q = ( U₂ + P₂V₂ ) – ( U₁ + P₁V₁ )

∆Q= h₂ – h₁

Therefore ,

∆Q = dh

and

dh = mc_pdT

The above result is valid for :

• Constant pressure, any gas

OR

• Ideal gas , any process

Hence , at constant pressure heat transfer is equal to the change in enthalpy.

Note :

What is Enthalpy?

In thermodynamics the term U +PV comes frequently and it is known as Enthalpy .

Enthalpy denotes the total energy content of the system and it is

(a) Property of the system

(b)Point function

(c) Exact differential

(d) cyclic integral is zero.

(c) isothermal process :

In Isothermal process , the temperature of the system remains constant .

i.e., T = constant

As we know that the internal energy is the function of temperature

Therefore , dU = 0

As , ∆Q= dU + ∆W

∆Q= ∆W

This is valid for Isothermal process only.

(d) Adiabatic process :

In adiabatic process the net heat transfer is zero .

∆Q= 0

(e) Polytropic process :

In Polytropic process , the relation PVⁿ = constant is followed .

∆Q = dU + ∆W

∆Q= mc_vdT + ( P₂V₂ – P₁V₁)/(1-n)

As it is valid for ideal gas only

we know that ,

cp – cv = R and cp/cv = ¥

Therefore ,

c_v = R/(¥-1) and cp = ¥R/(¥-1)

∆Q_poly = ∆W_poly × ( ¥- n )/(¥ – 1)

This is valid for polytropic process , with Polytropic index n .