A Level Multiple Choice

Specific Heat Capacity Questions

Q1. 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?

As it falls from the top of waterfall each kg of water transfers gravitational energy to heat.

Change in gravitational potential energy = mass x gravitational constant x change in height

ΔE_GPE = mgΔh

ΔE_GPE = 1 x 9.81 x 100

ΔE_GPE = 981 J

This GPE is transferred into heat energy, causing a rise in temperature

E_heat = mcΔT

981 = 1 x 4200 x ΔT

ΔT = 981/4200 = 0.23 K

Choice B

Q2. Axel 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?

E = mcΔT

m = 200g = 0.20 kg

ΔT = 79 - 23 = 56 °C

E = 0.20 x 4200 x 56

E = 47,040 J

t = 1 minute = 60s

P = E/t

P = 47,040/60

P = 784 W

Choice A