Physics CALORIMETRY

Specific Heat :

Specific heat of a substance is equal to heat gained or released by that substance to raise or fall its temperature by `1^0 C` for a unit mass of substance.
The gain or loss of heat is directly proportional to:

i. Mass of the substance `dQ prop m`

ii. Change in temperature of substance `dQ prop dT`

Or, `dQ prop mdT`

`dQ=ms dT=> Q = int dQ = int ms dT`

Where `S` is a constant and is known as the specific heat of the body.

`S=Q/(m Delta T)`

`S.I.` unit of specific heat's' is joule/kg- Kelvin and C.G.S. unit is `cal//gm^0C`.

Molar heat Capacity :

Molar heat capacity of a substance is equal to heat gain or released by that substance to raise or fall its temperature by `1^0 C` for a unit mole of substance. It is denoted by `'c'`.

Heat supplied or released by `'n'` mole of a substance is

`=> Q=int dQ=int nc dT` or `Q= nc Delta T` (if `c` is constant).

Heat Capacity or Thermal Capacity :

Heat capacity of a body is defined as the amount of heat required to raise its temperature by `1^0C`. It is denoted by `'C'`.

Heat supplied or released by body is

`=> Q=int C dT` or `Q=C Delta T` if , `C` is constant .

If `'m'` is the mass of the body and `'s'` is the specific heat then, heat capacity `C = ms`.

Water Equivalent :

If thermal capacity of a body is expressed in terms of mass of water it is called watere quivalent of the body, i.e., It is the amount of water which requires the same amount of heat for the same temperature rise as that of the object. it is denoted by `'W'`.

`ms Delta T=m_wS_w Delta t=> m_w =(ms)/(s_w)`

In calorie `s_w=1`

So, water equivalent `'W' = m_w = ms`.

Phase Change and Energy Related to Phase Change :

Heat supplied or released by a substance for the change of phase is

`Q=mL` where, `L=` latent heat.

Latent heat `(L)` :

the heat supplied to a substance which changes its state at constant temperature is called latent heat of the body.
S.I. unit of latent heat `'L'` is J/kg and C.G.S. unit is cal/gm.

Latent heat of fusion `(L_f)` :the heat supplied to a substance which changes it from solid to liquid state at its melting point and `1` atm pressure is called latent heat of fusion. Latent heat of fusion of ice is `80` cal/gm.

Latent heat of vaporization `(L_v)` :the heat supplied to substance which changes it from liquid to vapour state at its boiling point at `1` atm pressure is called latent heat of vaporization. Latent heat of vaporization of water is `540 ` cal/gm.

Journey from ice at `0^0C` to steam at `100^0C`

`Q=mL_V`

`Q=ms Delta T`

`Q=mL_F`

Suppose mass of ice is `m` gram. During state change from ice to water at `0^0C`, ice absorbed heat `(Q) = mL_F`. After that temperature of water increases and water consumes heat `(Q) = ms Delta T` (where `Delta T = 100^0C`). Now water at `100^0 C` converts
into steam at `100^0C` and absorbed heat `(Q) = mL_V`.