Find the quantity of heat needed to melt 100g of ice

Question

Find the quantity of heat needed to melt 100g of ice at -10°C into the water at 10°C.
(39900 J)
(Note: Specific heat of ice is $2100 J〖kg〗^{-1} K^{-1}$, the specific heat of water is $4200 J〖kg〗^{-1} K^{-1}$, Latent heat of fusion of ice is 336000 J$〖kg〗^{-1})$.

Accepted Answer

Solution: Mass of ice = m = 100 g = $\frac{100}{1000}$ = 0.1 kg

Specific heat of ice = c1 = $2100 J〖kg〗^{-1} K^{-1}$

Latent heat of fusion of ice = L = $336000 J〖kg〗^{-1}$

Specific heat of water = c = $4200 J〖kg〗^{-1} K^{-1}$

Quantity of heat required = Q =?

Case I:

Heat gained by ice from -10°C to 0°C

Q1 = $mc riangle T$

Q1 = $0.1 imes 2100 imes10$ = 2100 J

Case II:

Heat required for ice to melt = Q2 = mL

= $0.1 imes 336000$

Q2 = 33600 J

Case III:

The heat is required to raise the temperature of water from 0°C to 10°C

Q3= $mc riangle T$

Q3 = $0.1 imes 4200 imes 10$ = 4200 J

Total heat required = Q = Q1 + Q2 + Q3

Q = 2100 + 33600 + 4200

Q = 39900 J