14.2 Phase Changes

As part of a model village pyrotechnics display a 33 g iron ball bearing, cooled to a soecific initial temperature of −2.1592 °C, is dropped into a pool. The ball begins to accelerate uniformly from a height of 0.75 m above the surface of the pool with a velocity of 20 m s⁻¹.

Assume that the ball falls with a constant acceleration due to free fall but a thermal energy transfer takes place between the ball and the air.

The iron ball has a specific heat capacity of 440 J kg⁻¹ °C⁻¹.

Calculate the temperature of the ball immediately before it hits the water. 

The iron ball bearing from (a) falls into the pool. The pool has dimensions of 5 cm, 10 cm and 30 cm. The density of the water in the pool is 1030 kg m⁻³ and has a specific heat capacity of 4300 J kg⁻¹ °C⁻¹. The initial temperature of the water in the pool is 22.5173 °C.  

A professional cyclist of mass 50 kg is testing a new hydraulic brake system on his racing bike of mass 5 kg. He is travelling at a constant speed of 25 m s⁻¹ when he has to brake suddenly. 

The four brake discs on the bike each have a mass of 250 g, included in the mass of the bike. The specific heat capacity of the mineral oil in the brake system is 1.77 kJ kg⁻¹ °C⁻¹.

Calculate the overall increase in the temperature of the brake discs.

Explain how the temperature difference in the brake disc fluid can be reduced.

Water has a specific heat capacity of 4200 J kg⁻¹ °C⁻¹ and a boiling point of 100 °C. The boiling point of mineral oil is 300 °C.

Explain the statement the specific heat capacity of water is 4200 J kg^–1 K^–1.

The heater in an electric kettle has a power of 3.18 kW. 

When the water in the kettle is boiling at a steady rate, the mass of evaporated water in 1.5 minutes and the rate of loss of thermal energy to the surroundings is 500 W. The specific latent heat of vaporisation of water is 2.26 MJ kg^–1. 

A student places water in an ice cube tray of a freezer to calculate the specific latent heat of fusion of ice. 

700 g of water is placed in the ice cube tray at 0 °C and the freezer cools them to –3 °C. A total of 0.23 MJ of energy is removed from the water to turn it into ice at –3 °C. 

Specific heat capacity of ice = 2.1 kJ kg^–1 K^–1. 

Calculate the specific latent heat of fusion of ice.

Suggest why the specific latent heat of fusion of water is much less than the specific latent heat of vaporisation of water.

The energy required to boil water at 100 °C to steam at 100 °C is must greater than the energy required to melt ice at 0 °C to water at 0 °C. 

A heater supplies energy at a constant rate to 64 g of a substance. The variation with time of the temperature of the substance is shown in Fig. 1.1. The substance is perfectly insulated from its surroundings.

Calculate the ratio  .

Suggest what can be deduced from the fact that section X on the graph is steeper than section Y in Fig 1.1.

Calculate the energy released when 2.5 kg of water at 17 °C cools to 0 °C and then freezes to form ice, also at 0 °C. 

Specific heat capacity of water = 4200 J kg^–1 K^–1
Specific latent heat of fusion of ice = 3.4 × 10⁵ J kg^–1

Explain why it is more effective to cool ice packs by placing them in a box full of melting ice rather than in a box of water at an initial temperature of 0 °C.

The silica gel and water solution from the inside of an ice pack of mass 0.450 kg at a temperature of 2.00 °C are emptied and poured into a plastic beaker. The beaker has a mass of 0.210 kg and is initially at a temperature of 19.0 °C. 

Specific heat capacity of plastic = 1670 J kg^–1 K^–1
Specific heat capacity of silica gel and water = 6420 J kg^–1 K^–1

Calculate the final temperature, , of the silica gel and water solution when it reaches thermal equilibrium with the beaker.

Assume no heat is gained from or lost to the surroundings.

The silica gel and water solution, along with the beaker are cooled from to a temperature of 5 °C by adding ice at a temperature of 0 °C. 

Calculate the mass of ice added. 

Assume no heat is gained from or lost to the surroundings. 

Specific latent heat of fusion of ice = 3.34 × 10⁵ J kg^–1

Explain the meaning of the statement the specific heat capacity of water is 4200 J kg^–1 K^–1.

An engineer is designing an ice-making machine. Water will enter the device at 15°C and the ice cubes are to be cooled to –6°C before release. 

Show that about 0.3 MJ of energy must be removed from 0.75 kg of water at 15°C to change it into ice at –6°C.        

Specific heat capacity of water = 4.2 × 10³ J kg^–1 K^–1
Specific heat capacity of ice = 2.1 × 10³ J kg^–1 K^–1
Specific latent heat of fusion of ice = 3.3 × 10⁵ J kg^–1

The design brief requires that 1.25 kg of water is frozen in 240 s. 

Calculate the rate at which energy must be removed from the machine.

The specific latent heat of vaporisation of water is 2.3 × 10⁶ J kg^–1. 

Suggest why the specific latent heat of vaporisation of water is much greater than the specific latent heat of fusion of water.