3.1 Thermal Concepts

A meteorite of pure nickel with a constant mass of 3.9 kg falls to Earth and begins to accelerate uniformly from the atmosphere's edge at a height h_A = 225 km and velocity 95 m s⁻¹. Initially in the atmosphere, it accelerates, reaches a constant velocity and continues to fall. It falls into a circular pond of water at a temperature of 18 °C with a velocity of 125 m s⁻¹.

The pond has a radius of 3.5 m and a depth of 70 cm. The nickel has a specific heat capacity of 0.44 J g⁻¹ K⁻¹ and had a temperature of −270 °C before it started to fall.

The specific heat capacity of the water is 4200 J kg⁻¹ K⁻¹ and the density of the water is 1000 kg m⁻³. 

Determine the increase in the temperature of the water, assuming that the meteorite and the water reach thermal equilibrium and no thermal energy is lost to the surroundings. 

A car of mass 875 kg is travelling on a flat road at a constant speed of 35 m s⁻¹. An obstacle appears in the road, the brakes are applied and the car comes to a stop. 

The car has four brake disks and each has a mass of 1.3 kg. The specific heat capacity of the brake disk material is 460 J kg⁻¹ K⁻¹. 

Calculate the overall increase in the temperature of the disks. 

When brakes are applied in a car, incompressible brake fluid forces the brake pads into place. The brake fluid heats up because it is in contact with the brake pads. It must not boil, or it will compress and the brakes will not work. 

A certain brand of brake fluid uses a material called glycol. Engineers with the brand are investigating mixing some water with glycol to make the brake fluid less likely to overheat. 

Evaluate whether adding water to glycol will make the brake fluid safer from overheating. 

A car manufacturer is developing brakes that bring the car to a stop over the same distance whether the car is going up or downhill.

Cars P and Q are on a slope at an angle α to the horizontal and at a distance of y m apart. The cars have an identical mass, m, velocity, v and four identical brake pads of mass m_D. 

Determine an expression for the difference in temperature increase of the brake pads of each car when they both come to a stop after braking over a distance of .

An electrical immersion heater with a power of 5 kW is used to heat water flowing past it in a cylinder. The water flows through the heating cylinder at a rate of 0.11 kg s⁻¹. Valves at the beginning and end of the cylinder prevent the water from flowing backwards. 

The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

Calculate the rise in temperature of the water as it flows through the heater.

Assume all the energy is transferred to the water. 

A fault in the pump that pushes water through the heater causes the water to stop flowing. The valves at each end of the heating cylinder close and the water inside continues to heat. The closed cylinder has a length of 31.2 cm and a diameter of 12.6 cm.

The water temperature is 21.5 °C when the valves are shut. Water has a density of 1000 kg m⁻³. 

Calculate the time taken for the water to boil at 100 °C if the immersion heater continues supplying energy at the same rate. 

There are two main methods that are used to measure the specific heat capacity of liquids. 

Method A, Immersion Heater: involves submerging an immersion heater in the liquid to be tested.

Method B, Continuous Flow: involves flowing the liquid to be tested past a heater.

Discuss the two different methods for measuring the specific heat capacity of a liquid.

• Explain how a value for the specific heat capacity is obtained
• Explain any systematic problems with the methods, and how they will affect the final result
• Explain how a continuous flow method can compensate for energy lost as thermal radiation during the experiment

An unopened soda drinks can is cooled using an electric chiller that is powered using a USB connection with a laptop computer. The chiller is advertised as using 37 W of power and cools drinks to 12 °C from any room temperature and then maintains the drink at that temperature. 

A can of soda has a mass of 16 g when empty, and contains 324 g of soda. The can is a metal alloy that has a specific heat capacity of 800 J kg⁻¹ K⁻¹ and the soda has a specific heat capacity of 3700 J kg⁻¹ K⁻¹.

Calculate the time it takes to cool the can from a room temperature of 23 °C to 12 °C.

An alternative way to cool drinks is to add ice to them. Ice can be made in an ice maker. A particular model advertises that it can produce 15 kg of ice in 24 hours and requires 230 W when working. It produces ice cubes at a temperature of −5 °C. 

The specific latent heat of fusion of ice is 0.336 MJ kg⁻¹.

The specific heat capacity of ice is 2100 J kg⁻¹ K⁻¹.

The specific heat capacity of water is 4100 J kg⁻¹ K⁻¹.

Determine whether the ice cube maker or the electric chiller from part (a) is a more energy efficient method for cooling drinks from 23 °C to 12 °C. 

This question is about water as it changes state.

Water at constant pressure boils at a constant temperature.

Outline, in terms of the energy of the molecules, the reason for this.

In an experiment to measure the specific latent heat of vaporization of water, steam at 100°C was passed into water in an insulated container.

The following data are available.

• Initial mass of water in container = 0.260 kg
• Final mass of water in container = 0.278 kg
• Initial temperature of water in container = 20.4 °C
• Final temperature of water in container = 53.4 °C
• Specific heat capacity of water = 4.18 × 10³ J kg^–1 K^–1

Show that the specific latent heat of vaporization of water is about 1.8 × 10⁶ J kg^–1.

The accepted value of L is greater than that given in part (b).

Explain why, other than through experimental or calculation error, this is the case.

The insulated container is replaced with one made of iron and the experiment is repeated with the same starting temperature and masses of steam and water.

After a period of time, the container reaches thermal equilibrium with the water at a temperature of 30.7 °C. The specific heat capacity of iron is 447 J kg^–1 K^–1.

Assuming no energy is lost to the surroundings, calculate the mass of the container.

This question is about thermal energy transfers involved in sweating.

Distinguish between the concepts of temperature and internal energy.

An athlete loses 2.4 kg of water through sweat whilst training for 2 hours.

Estimate the rate of energy loss by the athlete due to sweating. The specific latent heat of vaporization of water is 2.3 × 10⁶ J kg^–1.

The athlete sits down to rest on an aluminium chair of mass 40 kg following her training session.

The temperature of the athlete is 37.8 °C and the temperature of the chair is 293 K. The specific heat capacity of aluminium is 900 J kg^–1 K^–1.

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Assume the athlete maintains a constant temperature.

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When the sweat evaporates from the athlete it turns from a liquid to a gas.

State, in terms of molecular structure and motion, two differences between a liquid and a gas.

This question is about a slowly melting iceberg.

Distinguish the difference between liquid water and solid ice, with reference to molecular motion and energy.

The following data is available regarding an iceberg:

• The iceberg has a density of 920 kg m^–3
• The temperature of the iceberg is –25 °C
• The volume of the iceberg is 78 000 m³
• The specific latent heat of fusion of ice is 3.3 × 10⁵ J kg^–1
• The specific heat capacity of ice is 2.1 × 10³ J kg^–1 K^–1

Calculate the energy required to melt the iceberg to form water at 0°C.

The Sun supplies thermal energy to the iceberg at an average rate of 450 W m^–-2. Assume that the iceberg has a consistent surface area of 312 m².

Estimate the time taken, in years, to melt the iceberg, assuming the melted water is immediately removed, and no heat is lost to the surroundings.

In reality, there is heat transferred between the sea, which is at a temperature greater than 0°C, and the iceberg.

Outline what effect this will have on the rate of melting of the iceberg.

This question is about an experiment to examine how the specific heat capacity of water varies with temperature.

Draw the line of best fit for the data.

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The experiment used water that reached a height of 40 cm in a cylindrical can of diameter 50 cm. The average density of water between 70 °C and 90 °C is 970 kg m^–3. 

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