What two components gain heat when ice is added to water?

Express it mathematically. (use appropriate symbols, not your actual numerical values.
- I know that the ice gains heat as well as the H2O from the ice, but i don't understand how to express it in the form of an equation.

Also, "What loses heat when ice is added to water? express it mathematically"

-The initial water used loses heat, but how is it expressed?

Much appreciated!

Well, here's a mathematically humorous way to express it:

Heat gained by the ice + Heat gained by the water from the ice = A big warm H2O party! 🎉

In more conventional notation, you could write it as:

Q_ice + Q_water = H2O celebration! 🎉

Just remember, Q_ice represents the heat gained by the ice, and Q_water represents the heat gained by the water from the ice.

When ice is added to water, there are two components that gain heat:

1. Ice: The heat gained by the ice to raise its temperature from its initial temperature, T_initial, to its melting point temperature, T_melting. We can express it mathematically as:

Q_ice = m_ice * c_ice * (T_melting - T_initial)

Where:
- Q_ice is the heat gained by the ice (in Joules).
- m_ice is the mass of the ice (in grams or kilograms).
- c_ice is the specific heat capacity of ice (in J/g·°C or J/kg·°C).
- T_melting is the melting point temperature of ice (in °C or Kelvin).
- T_initial is the initial temperature of the ice (in °C or Kelvin).

2. Water from the ice: The heat gained by the water that comes from the melted ice to raise its temperature from the melting point temperature, T_melting, to a final temperature, T_final. We can express it mathematically as:

Q_water = m_water * c_water * (T_final - T_melting)

Where:
- Q_water is the heat gained by the water (in Joules).
- m_water is the mass of the water (in grams or kilograms).
- c_water is the specific heat capacity of water (in J/g·°C or J/kg·°C).
- T_final is the final temperature of the water (in °C or Kelvin).

Note: It is important to use the appropriate units for mass and specific heat capacities to ensure consistent calculations.

When ice is added to water, heat is gained by two components: the ice itself and the surrounding water. To express this mathematically, we can use the principle of conservation of energy.

Let's denote the heat gained by the ice as Q_ice and the heat gained by the water as Q_water.

According to the principle of conservation of energy, the total heat gained by the system (ice + water) is equal to zero. Therefore, we can write the equation:

Q_ice + Q_water = 0

This equation states that the heat gained by the ice plus the heat gained by the water is equal to zero since energy is conserved. Note that this equation assumes no heat is lost to the surroundings.

The positive sign for Q_ice indicates that heat is gained by the ice, and the negative sign for Q_water indicates that heat is lost by the water (since Q_water is the negative counterpart of Q_ice when summing to zero).

So, mathematically, the equation is:
Q_ice + (-Q_water) = 0

1. mass ice x heat fusion ice to melt ice.

2. mass water from ice x specific heat water x (Tfinal-Tinitial) to heat water from ice.
3. water there initially loses heat.
mass x specific heat water x (Tfinal-Tinitial)