Latent Heat Calculations

Latent Heat

This image will seem relvant soon I promise

When overnight temperatures drop below 0^oC, orange farmers will intentionally spray their crops with water.

It's not because they've lost their minds from the monotony of orange farming.

Let's figure out why. Its all to do with thermal physics (big surprise).

Relationships we already know

•  $U=K.E.\ +\ P.E.$  

•  $\Delta U=Q-W$  

•  $Q=mc\Delta T$  

Multiple Choice

To increase the temperature of an object we need to increase the _______ of the particles

• Average kinetic energy

• Average potential energy

Open Ended

What happens if the average potential energy of the particles is increased instead?

Multiple Choice

Which state of matter has particles with the highest potential energy?

• Solid

• Liquid

• Gas

Multiple Choice

An (ideal) gas has a potential energy closest to:

• -1000 J

• 0 J

• 1000 J

Potential Energy of States of matter

• The particles in solids and liquids are attracted to each other (like the top pair of magnets)

• So we would need to do work on them/transfer energy into the system/use energy to separate them

• So, solids and liquids have negative potential energy

Potential Energy of States of matter

• Solids have the least/most negative potential energy

• Liquids are in the middle

• Gases have the most/least negative potential energy

Multiple Choice

Imagine you have a half melted cup of slushie (ice and water). If the potential energy of the ice/water mixture is increased then

• The water will freeze

• The ice will melt

Non-SI units

Also not SI units

Latent Heat

•  $Q=mL_{fusion}$  

•  $Q=mL_{vapour}$  

• Generally,  $L_{vapour}>L_{fusion}$  

Open Ended

Use the graph to estimate the latent heat of fusion for water

Open Ended

Use the graph to estimate the latent heat of vapourisation for water

We were pretty close!

• We must add 334 kJ of energy to 1 kg of ice at 0^oC in order to 'melt' it

• We must add 2260 kJ of energy to 1kg of water at 100^oC in order to turn it into steam

It works in reverse too

• If 1 kg of steam at 100^oC is condensed into water it will release 2260 kJ of energy

• If 1kg of water at 0^oC freezes into ice it will release 334 kJ of energy

Also not SI units

That's why farmers spray budding oranges with water in freezing temperatures

When the water freezes it releases thermal energy, some of which heats the delicate orange flower.

Your turn (somewhat challenging)

Three ice cubes are used to chill a glass of water at 20^oC with a mass of m_water=0.25 kg. The ice is at 0^oC and each ice cube has a mass of 6.0g. Assume that the water is kept in a foam container (so that heat loss can be ignored).

What is the final temperature of the glass of water once the ice has melted?

This is a hard question so lets break it down a bit.

Open Ended

Three ice cubes are used to chill a glass of water at 20^oC with a mass of m_water=0.25 kg. The ice is at 0^oC and each ice cube has a mass of 6.0g. Assume that the water is kept in a foam container (so that heat loss can be ignored).

Lets call mass of the ice 'm'

Mass of the water 'M'

Latent heat of fusion for water 'L'

Specific heat capacity of water 'c'

Final temperature of glass of water 'T'

Write an expression for the total heat transferred to the ice. Assume this is a strictly positive value.

Q_ice=..........

Open Ended

Three ice cubes are used to chill a glass of water at 20^oC with a mass of m_water=0.25 kg. The ice is at 0^oC and each ice cube has a mass of 6.0g. Assume that the water is kept in a foam container (so that heat loss can be ignored).

Lets call mass of the ice 'm'

Mass of the water 'M'

Latent heat of fusion for water 'L'

Specific heat capacity of water 'c'

Final temperature of glass of water 'T'

Write an expression for the total heat transferred from the water. Assume this is a strictly positive value.

Q_water=..........

Multiple Choice

We are assuming that the glass of water and the ice cubes are a thermally isolated system. This means that

(Note: |Q| means 'absolute value of Q' a.k.a the 'size' of Q, or 'ignore any negative signs')

• |Q_ice|<|Q_water|

• |Q_ice|=|Q_water|

• |Q_ice|>|Q_water|

Open Ended

Three ice cubes are used to chill a glass of water at 20^oC with a mass of m_water=0.25 kg. The ice is at 0^oC and each ice cube has a mass of 6.0g. Assume that the water is kept in a foam container (so that heat loss can be ignored).

Use your results from the previous slides to calculate the final temperature of the water (find T).