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Specific heat capacity is a fundamental concept in thermodynamics that describes how much energy a substance can absorb or release as its temperature changes. It's the amount of heat energy required to change the temperature of one gram of a substance by one degree Celsius. For water, this value is approximately \(4.186 \, \text{J/g°C}\).

This property makes water an excellent medium for thermal regulation, such as preventing rapid temperature drops in the garage environment by absorbing heat. When water at \(20^{\circ} \mathrm{C}\) cools to \(0^{\circ} \mathrm{C}\), the energy transferred can be calculated with the formula: \[Q = mc\Delta T\]

Where:

• \(m\) is the mass, in grams, of the water which in this case is \(125,000 \, \text{g}\).
• \(c\) is the specific heat capacity of water \(4.186 \, \text{J/g°C}\).
• \(\Delta T\) is the temperature change \(20°C \to 0°C\).

This results in a calculated value of \(10,465,000 \, \text{J}\) being released as the water temperature drops to just freezing.

The latent heat of fusion is the energy required to change a substance from solid to liquid (or vice versa) at a constant temperature. For water, this is \(334,000 \, \text{J/kg}\).

This property is crucial in the case of the water's transition from liquid to solid as it involves energy transfer without a temperature change. Here's the reasoning:

• When the water reaches \(0^{\circ} \text{C}\), it must release additional energy for the phase change from liquid to ice.
• This is calculated with \(Q = mL\), where \(m\) is mass and \(L\) is the latent heat of fusion.
• For the given problem, the energy required for the complete phase change is \(41,750,000 \, \text{J}\).

It means even when the temperature is held constant at freezing, considerable energy is still released, important for keeping the garage above freezing temperature for an extended period.

Energy transfer in thermodynamics, especially dealing with water, is about the exchange of energy due to both temperature change and phase transitions. Combined, these calculations give us insights into how much energy the water needs to expel to freeze.

When adding the energy needed to cool the water and then freeze it, the total energy transferred to the surroundings is:

• From cooling: \(10,465,000 \, \text{J}\)
• From freezing: \(41,750,000 \, \text{J}\)

So, the entire energy transferred is \(52,215,000 \, \text{J}\).

This comprehensive energy exchange keeps the garage from dipping too low in temperature. The lowest possible temperature that can be achieved is maintained at \(0^{\circ} \text{C}\) until all the water is frozen, making it an effective temperature buffer.