Determination of specific latent heat of fusion of ice by the method of mixtures

In the experiment above, let:

• $m_{1}$: The mass of an empty calorimeter with a stirrer
• $m_{2}$: Mass of the calorimeter with a quantity of water
• $\theta_{1}$: The initial temperature of the water
• $\theta_{2}$: Minimum temperature of the mixture when mixed with ice
• $m_{3}$: Mass of the calorimeter with final contents
• $c_{w}$: Specific heat capacity of water
• $c$: Specific heat capacity of calorimeter metal
• $L$: Specific latent heat of fusion of ice

Then since $0^{\circ}C<\theta_{2}<\theta_{1}$, assuming that no heat was absorbed from the surroundings during mixing:

Heat gained by ice = Heat lost by water and calorimeter (with stirrer)

1. Measure the mass $(m_{1})$ of the calorimeter with the stirrer.
2. Fill about two thirds of the calorimeter with water at room temperature and measure its mass $(m_{2})$ again. Measure also the temperature $(\theta_{1})$ of the water.
3. Wipe out water from small pieces of ice using filter paper and put those one by one into the water in the calorimeter while stirring, taking care to insert one piece after the previous one has dissolved. Use a square-net stirrer to prevent the ice from floating in water.
4. When the temperature of the water has fallen sufficiently (by about $5^{\circ}C)$ stop adding ice, stir the mixture well and record the lowest temperature of the mixture $(\theta_{2})$.
5. Finally measure the mass of the calorimeter with its contents again $(m_{3})$.
6. Substitute values of $m_{1}$, $m_{2}$, $\theta_{1}$, $\theta_{2}$ and standard values for $c$ and $c_{w}$ in the expression given in the theory and calculate the value of $L$.