Question

35g of water at 0 degree Celsius is completely converted to ice at 0 degree Celsius by extracting 2 kilo joules of heat from it. If the specific heat capacity of water is 4200 joules per kilogram per Kelvin, calculate the specific latent heat of fusion of ice

Answer 1

The amount of heat extracting from the water can be written as follows:

$$Q=Q_1+Q_2,$$

here, $Q_1$ is the amount of heat that should be extracted to cool the water from $10^{\circ}C$ to $0^{\circ}C$, $Q_2$ is the amount of heat that should be extracted to convert water from $0^{\circ}C$ to ice at $0^{\circ}C$.

Then, we can write:

$$Q=mc\Delta T+mL_f.$$

From this equation we can find the specific latent heat of fusion of ice:

$$L_f=\dfrac{Q-mc\Delta T}{m},$$ L_f=\dfrac{2\cdot10^3\ J-0.035\ kg\cdot4200\ \dfrac{J}{kg\cdot \!^{\circ}C}\cdot10^{\circ}C}{0.035\ kg}=1.5\cdot10^4\ \dfrac{J}{kg}.