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 ( V_{2 } – V_{1 } )

and dU = U_{2} – U_{1}

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

∆Q = U_{2}-U_{1} +P(V_{2}-V_{1})

∆Q = ( U_{2 }+ P_{2}V_{2} ) – ( U_{1} + P_{1}V_{1} )

∆Q= h_{2} – h_{1}

Therefore ,

## ∆Q = dh

and

## dh = mc_{p}dT

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 PV^{n } = constant is followed .

∆Q = dU + ∆W

∆Q= mc_{v}dT + ( P_{2}V_{2} – P_{1}V_{1})/(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 .