P.3.6.2.1 Thermal energy transfer

A continuous stream of water falls through a vertical distance of 100 m. Assume no thermal energy is transferred to the surroundings. The specific heat capacity of water is 4200 J kg^–1 K^–1.

What is the temperature difference of the water between the top and bottom of the waterfall?

• 0.023 K

• 0.23 K

• 2.3 K

• 4.3 K

A student measures the power of a microwave oven. He places 200 g of water at 23 °C into the microwave and heats it on full power for 1 minute. When he removes it, the temperature of the water is 79 °C. The specific heat capacity of water is 4200 J kg^–1 K^–1.

What is the average rate at which thermal energy is gained by the water?

• 780 W

• 840 W

• 1.1 kW

• 4.6 kW

An ice cube of mass 0.010 kg at a temperature of 0 °C is dropped into a cup containing 0.10 kg of water at a temperature of 15 °C.

What is the maximum estimated change in temperature of the contents of the cup?

specific heat capacity of water = 4200 J kg⁻¹ K⁻¹

specific latent heat of fusion of ice = 3.4 × 10⁵ J kg−1

• 1.5 K

• 8.7 K

• 13.5 K

• 15.0 K

A liquid flows continuously through a chamber that contains an electric heater. When the steady state is reached, the liquid leaving the chamber is at a higher temperature than the liquid entering the chamber. The difference in temperature is Δt.

Which of the following will increase Δt with no other change?

• Increasing the volume flow rate of the liquid

• Changing the liquid to one with a lower specific heat capacity

• Using a heating element with a higher resistance

• Changing the liquid to one that has a higher density

The temperature of a hot liquid in a container falls at a rate of 2 K per minute just before it begins to solidify. The temperature then remains steady for 20 minutes by which time all the liquid has all solidified.

What is the quantity shown?

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• 
• 10 K^–1

• 40 K^–1

A car of mass M travelling at speed V comes to rest using its brakes. Energy is dissipated in the brake discs of total mass m and specific heat capacity c. The rise in temperature of the brake discs can be estimated from

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A raindrop of mass m falls to the ground at its terminal speed v. The specific heat capacity of water is c and the acceleration of free fall is g. Given that 25% of the energy is retained in the raindrop when it strikes the ground, what is the rise in temperature of the raindrop?

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A 1.0 kΩ resistor is thermally insulated and a potential difference of 6.0 V is applied to it for 2.0 minutes. The thermal capacity of the resistor is 9.0 J K^–1. The rise in temperature, in K, is

• 1.3 × 10^–3

• 8.0 × 10^–3

• 0.48

• 0.80