Heat and work are the forms of energy , in the previous post we had discussed about the work transfer.

The form of energy which flows due to the temperature difference is **heat** and they phenomenon of its flow is * heat transfer* .

### Heat transfer is :

- Path function
- Boundary phenomenon
- Transient phenomenon
- Not a property of a system
- Inexact differential
- Cyclic integral is non zero

Heat transfer is always written in form :

∆Q ( ✓)

~~dQ ~~(×), bcoz heat transfer is Inexact differential.

## Heat Capacity : ( C )

The amount of heat required to raise the temperature of system by unit degree is heat capacity and it is denoted by C .

C = ∆ Q / ( dT)

∆ Q= C × dT

OR

*∆** Q = CdT*

*∆*

*Q = CdT*

#### C is a coefficient called heat capacity it’s magnitude depends upon:

- Size of the system
- State of the system
- Composition of the system

#### Unit of C = KJ/ kelvin.

## Specific heat : (c)

It is amount of required to rise the temperature of unit mass of substance by one unit .

It is denoted by c ( small alphabet).

Unit of c = KJ/ (Kg – kelvin)

c= ∆ Q / ( M .dT)

∆ Q= M c × dT

## ∆ Q = McdT

Here ,

∆Q = amount of heat .

M = mass of substance

c = specific heat

C = heat capacity

dT = change in temperature

As we know that the amount of heat is path function , therefore specific heat is also a path function and therefore depend on the constant volume and constant pressure conditions , that helps in defining the path of the system.

Therefore ,

#### There are two types of specific heat :

(a) c_{p }= specific heat at constant pressure

(b) c_{v } = specific heat at constant volume

These two specific heats have a relationship which is called **Meyer’s Relationship** , and it valid only for :

(a) unit mass

(b) ideal gas

## c_{p}– c_{v }= R

For Heat capacity Meyer’s Relationship :

**C**_{P }– C_{V} = R

_{P }– C

_{V}= R

Here

C_{p } = heat capacity at constant pressure

C_{v }= heat capacity at constant volume

And from the Meyer’s Relationship it is clear that the

C_{p }>C_{v }

## Ratio of Cp / Cv :

The ratio of c_{p }/ c_{v }is called specific heat ratio and is denoted by ¥ ( gamma)

¥ = specific heat ratio

Gas | ¥ |

Triatomic | 1.33 |

Diatomic | 1.4 |

Monoatomic | 1.67 |

## Sensible heat –

The amount of heat required by any thermodynamic system to change the temperature of the substance is Sensible heat .

## Latent heat –

The amount of heat required by the system or a body to change its phase without any interference in temperature is Latent heat .

Therefore , the specific heat of phase change is infinity.

Because , dT = 0 ;

Therefore , c ~ infinity.

For example :