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# Specific heat and latent heat of fusion and vaporization

Defining specific heat, heat of fusion, and heat of vaporization. How to calculate the amount of heat to change the temperature of water and the energy required to change for a phase change.  Created by David SantoPietro.

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• Just to be clear, the overall Q required to turn -40c to 160 will be the addition of all five Q values at each point on the graph + Q5? • Why is the heat of fusion different from the heat of vaporization? •   good question

Think about the spacing of the molecules during phase change.

Latent heat of fusion: Solid to liquid...not much space increase
Latent heat of vapourisation: Liquid to gas...big space increase

The larger distance between the molecules means much larger potential energy
More energy is required, therefore, to turn the liquid into gas to provide that potential energy between the molecules
• Is it coincidence that the specific heat of water is approximately twice that of both ice and steam? • Well, ice happens to be a bit special as water is denser than it, unlike how it is for most solids. And since the liquid state is denser than both the gas and solid, that is likely (I could be wrong since I don't know how to mathematically prove this) the reason why water's specific heat is greater than both.

And since ice is denser than vapour, phase change from ice to water has slightly higher heat requirement than that for phase change of water to vapour.
• what is heat capacity and specific heat capacity • Heat Capacity: ratio of the amount of energy absorbed to the associated temperature rise.
•Example: if it takes 10 calories to raise the temperature of a glass of water by 2 °C, then the heat capacity of the glass of water is 10 calories/2°C = 5 calories per °C.

•Specific Heat: the heat capacity of a substance per unit mass
•Example: for water, it takes 1 calorie to raise the temperature of 1 gram of water by 1°C. So the specific heat for water is 1cal/gram °C
• what is the meaning of latent heat in fusion and in vaporization? • Think of it this way: when a pot of water is kept boiling, the temperature remains at 100C until the last drop evaporates, because all the heat being added to the liquid is absorbed as latent heat of vaporization and carried away by the escaping vapor molecules
• Ice at 273 K has more cooling effect than water at 273 K. Why? • because when ice changes state to water at this temperature it must absorb a certain amount of heat from it's surroundings. So unlike liquid water at 273 K, that only requires 4.18J/gC to raise it one degree, the ice is going to require more energy and draw that energy from its surrounding, making the surroundings even more cool.
• In the very last example to turn the block of ice into steam, wouldn't you have to add all the heat values up? Because 361,800J is much smaller than the other heat values, such as the phase changes. • 0.5kg of ice at -5degC is put into a vessel containing 2kg of water at 15deg C and mixed together, the result being a mixture of ice and water at 0degC.Calculate the final masses of ice and water, taking the water equivalent of the vessel as 0.15kg.The specific heat of ice is 2.04kJ/kg/K and the latent heat of fusion is 335kJ/kg. • heat to warm ice + heat to melt ice + heat to cool water + heat to cool vessel = 0
q₁ + q₂ + q₃ + q₄ = 0
m₁c₁ΔT₁ + m₁ΔfusH + m₃c₃ΔT₃ + m₄c₃ΔT₃ = 0
q₁ =0.5 kg × 2.04 kJ·K⁻¹kg⁻¹ × (0 –(-5)) K = 5.1 kJ
q₂ = m₁ × 335 kJ·kg⁻¹
q₃ = 2 kg × 4.184 kJ·K⁻¹kg⁻¹ × (0-15) K = -124.4 kJ
q₄ = 0.15 kg × 4.184 kJ·K⁻¹mol⁻¹ × (0-15) K = -9.4 kJ

5.1 kJ + 335m₁ kJ·kg⁻¹ - 125.5 kJ - 9.4 kJ = 0
5.1 + 335m₁ kg⁻¹ - 125.5 - 9.4 = 0
335m₁ kg⁻¹ = 124.4 + 9.4 – 5.1 = 129.8
m₁ = 129.8/335 kg⁻¹ = 0.39 kg

So, 0.39 kg of ice have melted.
∴ The mass of the remaining ice is (0.5 – 0.39) kg = 0.1 kg
• I don't understand how the temperature can stay constant during a phase change if the phase change releases heat anyway. Wouldn't the heat released from the phase change affect the overall temperature? • To add on to what Andrew M said, I like to think about phase changes as converting the incoming thermal energy (when you're heating something up) to potential/phase energy. In a certain phase, such a solid, the particles can only move so much because its IMF is holding them together. At a certain point, the incoming thermal energy can't make the particles move any faster/KE can't increase because of the phase it's in. Instead, the energy is converted to phase energy and allows the particles to break free of their IMF. When the energy is converted to phase energy, you're right in that there is a tiny drop in temperature but it's replaced almost immediately when you're continuously adding energy into a substance. 