Calorimetry Simulation: Ice & Water

Modify initial temperature and mass, then drop the ice cube. Observe the final temperature and the melting and freezing of the substances!

What even is heat?

Heat is just thermal energy (think back to potential and kinetic energy). It is dependent on the mass of the substance, its specific heat capacity (a constant per material type, ex. cardboard is used on coffee cups because they have high heat capacities), and temperature.

When a change in state occurs, such as melting, more energy is required to make that "jump" known as latent heat. This is known as the energy required to change the state of 1kg of a given material.

What is happening?

When two substances come in contact with different temperatures, they seek to find an equilibrium with same temperature. To find that final temperature, we can simply set the heat lost by the hotter object equal to negative heat gained by the cooler object.

$$Q = mc \Delta T$$ $$Q_{fusion} = mL$$ $$ Q_{ice} = -Q_{water}$$ and some constants...

$$c_{ice} = 2.2 \frac{KJ}{kgK}$$ $$c_{water} = 4.2 \frac{kJ}{kgK}$$ $$L_{fusion} = 334 \frac{J}{g}$$

$$Q_1 = m_ic_i \Delta T$$ $$Q_2 = m_iL_f$$ $$Q_3 = m_wc_w \Delta T$$ $$Q_2 = m_wL_f$$

Deriving math in the simulation

To find whether the ice will melt, then warm up, or water freeze, then cool down, you have to deduce an equation for heat transfer. This can be done simply as shown on the left.

$Q_1 = -Q_3$ means both temperatures meet at 0 celsius.

$Q_1 < -Q_3 \space \And \space Q_1 + Q_2 >= -Q_3$ means some or all ice will melt.

$Q_1 + Q_2 < -Q_3$ means the melted ice will also warm up.

Substitute the heats to find what happens when water cools down. Note that since heat stops transfering at same temperatures, ice melting and water freezing cannot happen in the same process.