## Latent Heat of Fusion Formula :

Latent heat of fusion Q_{(J/g)} In joule per gram is equal to the product of the mass of body m_{(kg) }in kilogram is multiply by specific latent heat of fusion L_{(J/g) }joule per gram in the addition of mass of body and the specific latent heat of fusion c_{ (J) }in joule and the temperature change during heat absorption Δt_{(J)}.Hence the Latent Heat Of Fusion Formula has been written as,

**Q _{(J/g)} = m_{(kg)} L_{(J/g)} + m_{(kg)} c_{ (J) }Δt_{(J)}**

where,

Q→ latent heat of fusion J/g.

m→ mass of body in kg.

L →specific latent heat of fusion in J/g.

c →specific heat of body in J.

Δt→ temperature change during heat absorption (W).

## Sample Problems :

### Example 1:

Calculate the specific heat of metal, given that the latent heat of steam = 550 cal/g? In a piece of metal at 30^{o}C has a mass of 70g. When it is immersed in a current of steam at 100^{∘}C, 0.6g of steam is condensed on it.

### Solution :

Let c be the specific heat of the metal.

Heat gained by the metal

Q = m c Δt

Q = 70 × c × (100 – 30)

Q = 70 × c × 70 cal

The heat released by the steam

Q = m × L

Q = 0.6 × 550 cal

By the principle of mixtures,

Heat given is equal to Heat taken

0.6 × 550 = 70 × c ×70

c = 1.484 cal/g ^{∘}C .

### Example 2

Calculate the specific heat of metal, given that the latent heat of steam = 580 cal/g? In a piece of metal at 40^{o}C has a mass of 60g. When it is immersed in a current of steam at 100^{∘}C, 0.7g of steam is condensed on it.

### Solution:

Let c be the specific heat of the metal.

Heat gained by the metal

Q = m c Δt

Q = 60 × c × (100 – 40)

Q = 60 × c × 60 cal

The heat released by the steam

Q = m × L

Q = 0.7 × 580 cal

By the principle of mixtures,

Heat given is equal to Heat taken

0.7 × 580 = 60 × c ×60

c = 8.8669 cal/g ^{∘}C .