Specific heat capacity

A metal block of mass m is at temperature T₀. An electrical heater of constant power P heats the block for time t and it reaches a temperature T₁. The overall efficiency of the process is x.

Which expression gives the correct value of c, specific heat capacity of the block?

Plot the missing data point on the graph above and draw a line of best fit.

Describe the relationship suggested by the graph and suggest an explanation.

This question is about comparing two methods for storing energy.

A proposed method for storing energy uses trucks powered by electric motors.

The trucks carry sand up a mountain, storing surplus energy as gravitational potential energy.

When the energy needs to be released, they carry the sand back down the mountain, converting the gravitational potential energy into chemical energy stored in a battery.

Explain how an electrical generator in the truck could use electromagnetic induction to convert gravitational potential energy into chemical energy stored in a battery.

A second proposed method for storing energy uses a tank of wax.

The wax is heated using an electrical heater, storing surplus energy as internal energy of the wax. The wax increases in temperature and melts as it is heated.

When the energy needs to be released, the wax is allowed to cool, converting the internal energy of the wax into thermal energy.

Explain, in terms of the particles in the wax, how energy is stored when it is heated.

A 3D printer can manufacture small objects.

Some 3D printers use polylactic acid (PLA). PLA is supplied in the form of long filaments. The 3D printer melts the PLA and builds up the shape of the desired object in layers.

The electrical supply to the heater in the printer has an e.m.f., , of 12 V. The power of the heater is 40 W.

Calculate the resistance, R, of the heater.

The specific latent heat of fusion of PLA is 9.4 × 10⁴ J kg^–1 and its melting point is 160 °C. (b)

Define specific latent heat of fusion.

Calculate the maximum mass m of PLA that the heater could melt in one minute.

Explain why the printing process is slower in practice than your answer to (ii) suggests.

High-energy X-ray photons can destroy living cells. In radiotherapy, these photons are targeted at cancer cells.

The radiation dose is the amount of energy that a patient’s body absorbs from the high-energy X-ray photons.

Fig. 6.2 shows how this dose changes with depth below the surface of the skin.

The dose initially rises with depth because the high-energy X-ray photons produce electrons and positrons as they pass through the body. These electrons and positrons are quickly absorbed, increasing the dose.

Explain why high-energy X-ray photons produce electrons and positrons as they pass through the body.

*(ii) A 3D object called a bolus is used in radiotherapy for patients with skin cancer. A bolus targets the maximum radiation dose near the surface of the skin. So using a bolus makes the radiotherapy more effective.

A bolus can be made from PLA using a 3D printer. The bolus must fit the shape of the patient’s body exactly. This shape is found beforehand by giving the patient either a CAT scan or a PET scan.

• Explain how CAT scans and PET scans work.

• Discuss the advantages and disadvantages of having a scan to produce a bolus for radiotherapy.

Describe the origin of the microwave background radiation.

The figure below shows how the intensity of the microwave background radiation varies with its wavelength .

The peak intensity is at a wavelength of 1.1 mm.

This spectrum of microwave background radiation changes with temperature according to Wien’s displacement law.

Suggest and explain how the spectrum might have looked in the distant past. You may draw on the figure to support your answer.

Calculate the energy of a photon which has a wavelength of 1.1 mm.

Estimate the number of photons of microwave background radiation incident per second on the back of your hand.

Assume that all emitted photons have the energy calculated in (ii), and that the back of your hand has a surface area of 150 cm².

number of photons per second =........ s^–1

A heater is used to heat water in a beaker.

Before switching on, the metal heater and the water are both at room temperature.

Describe the motion of the atoms of the metal heater and of the water molecules.

* A student is carrying out an experiment to determine the specific latent heat of fusion L_f of ice. The student has two sets of apparatus next to each other on the laboratory bench, as shown in Fig. 17.1 and Fig. 17.2.

Both funnels are identical and have the same mass of crushed ice at 0 C.

The current in the heater is 5.0 A and the potential difference across it is 12 V.

Fig. 17.3 shows the variation of mass of water m collected in each beaker with time t.

Describe and explain the shape of the two graphs in Fig. 17.3 and use them to determine the

specific latent heat of fusion L_f of ice.

Additional answer space if required

Use the kinetic theory of matter to describe the solid phase (section AB) and the liquid phase (section CD) in terms of the motion and arrangement of the molecules of the substance.

Use Fig. 21 to explain how the specific heat capacity of the liquid compares with the specific heat capacity of the solid.

State what is meant by the internal energy of the substance.

Beyond the point E in Fig. 21, the substance behaves as an ideal gas.

The mass of a gas molecule is 4.8 × 10^–26 kg. (i) Calculate the root mean square speed of the gas molecules at a temperature of 250 °C.

root mean square speed =........ m s^–1

Calculate the internal energy of 1.3 moles of the gas at 250 °C.

A plastic kettle is filled with 0.60 kg of water at a temperature of 20 °C. A 2.2 kW electric heater is used to heat the water for a time of 4.0 minutes.

Calculate the total energy supplied by the heater during the time of 4.0 minutes.

The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹ and the specific latent heat of (b) vaporisation of water is 2.3 × 10⁶ J kg⁻¹. The boiling point of water is 100 °C.

Calculate the mass of water remaining in the kettle after 4.0 minutes. Assume that all the thermal energy from the heater is transferred to the water.