Thermal Energy Transfers (HL IB Physics)

A solid material of mass m is being heated. The heater applies a constant power of 150m to the solid, which has a specific heat capacity of 1.8 × 10³ J kg^–1 K^–1. The graph below shows how the temperature of the material varies with time as the solid melts and becomes a liquid.

What is the specific latent heat of fusion of the substance?

Liquid iron solidifies without a change in temperature.

Which of the following is correct for the molecules in the solid phase compared with molecules in the liquid phase?

A liquid is initially at its boiling point. Energy is continuously supplied to the liquid at a uniform rate until it has completely evaporated.

Which graph shows how the temperature of the liquid, T, varies with the energy, Q, supplied to the liquid?

In a refrigerator, 2 kg of water cools from 30 °C to 0 °C and then freezes to form ice also at 0 °C. The whole process takes 4000 seconds.

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

The specific latent heat of fusion of ice is 3.4 × 10⁵ J kg⁻¹.

What is the power required by the refrigerator during this process?

A 2.1 kW kettle supplies energy to a water of mass 1 kg. The initial temperature of the water is 20 °C. The specific heat capacity of water can be taken to be 4200 J kg^–1 K^–1.

How long does it take for the water to start boiling?

A substance loses energy at a constant rate. The graph shows how the temperature, T, of the substance varies with time, t, as the state of the substance changes from liquid to solid. 

What can be deduced about this substance from the graph shown?

Aluminium melts at 660 °C. A mass m of solid aluminium is initially at a temperature of 645 °C. The aluminium is heated and melts into liquid aluminium and continues to be heated up to a final temperature of 720 °C.

• Specific latent heat of fusion of aluminium = L_f
• Specific heat capacity of solid aluminium = c_S
• Specific heat capacity of liquid aluminium = c_L

Which expression gives the energy needed for this change to occur?

The graph shows how the temperature T of a liquid varies with energy Q supplied to the liquid at a constant rate P.

The gradient of the graph is z and the liquid has a specific heat capacity, c.

What is the mass of the liquid?

A sealed cylinder contains water at 10 °C and ice at 0 °C. The system has been thermally isolated from the surroundings. The ice and the water reach thermal equilibrium.

What happens to the total internal energy of the system in order for equilibrium to be reached?

Objects with absolute temperature can lose energy through

1. convection
2. conduction
3. radiation

Equipment is tested on Earth for use on the surface of Mars. How will the equipment lose energy in the two locations?

The black body temperature of Venus is 90% of the black body temperature of Earth.

Which of the following correctly shows the ratio:

A black body has absolute temperature T and surface area A. The total power radiated by the body is P. What is the value of power if the surface area is reduced to one third of A, and the temperature increased to three times T?

1 kg of water at 20 °C cools to 0 °C and then freezes to form ice, also at 0 °C.

What is the energy released during this process?

You may use the following values:

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

Heat energy is supplied at a constant rate to a solid material with a specific heat capacity of 1.92 × 10³ J kg⁻¹ K⁻¹.

What is the specific latent heat of fusion of the substance?

The temperature of 500 g of water decreases by ΔT °C when placed in a fridge for 10 minutes. This container of water is then removed and a second container of mass 250 g and temperature 25 °C is placed in the same fridge for 20 minutes. 

Assume that the containers holding the water are identical and do not emit or absorb energy. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹.

What is the final temperature of the second container of water after 20 minutes?

An engine goes through 6000 cycles every minute. To maintain a constant working temperature, 152 J of energy must be removed by a coolant during each complete cycle of the engine. The temperature of the coolant rises by 20 °C as it passes through the engine. 

The specific heat capacity of the coolant is 3.8 × 10³ J kg⁻¹ K⁻¹ and the density is 1000 kg m⁻³.

What is the volume of the coolant that flows through the engine in one second?

A glass beaker of water contains an immersion heater completely submerged by the water and is placed on the right-hand side of a two-pan balance. The heater boils the water at    100 °C and is connected to a kWh meter. When the water starts to boil standard masses are added to the left-hand side of the balance so it is in equilibrium with the water. At this moment the reading on the meter is 11.3 kWh. 

A 400 g mass is then removed from the left-hand side of the balance, causing it to tilt. As the water boils off the right pan rises until it is once again in equilibrium. When this happens the new reading on the meter is 11.5 kWh.

What is the specific latent heat of vaporisation of the steam if the heater is 50% efficient?

A spring in a ball point pen has a mass of 0.10 g and a specific heat capacity of 400 J kg⁻¹ K⁻¹ and a spring constant k = 200 N m⁻¹. To open or close the nib of the pen the spring is compressed by 8 mm. Upon release 5% of the elastic potential energy stored is converted into heat energy in the spring.

How many times must the spring be compressed and released to cause the temperature of the pen to increase by 2 °C?

Assume that no heat is lost from the pen. 

An ice cube of mass m_i and temperature −T_i is dropped into a glass of water of mass m_w and temperature T_w. The specific heat capacity of ice is c_i and the specific latent heat of fusion of ice is L_i. The specific heat capacity of water is c_w.

What is the final temperature of the water?

A sample of a solid, with mass m and specific heat capacity c, is heated with a heater of constant power.

What is the power of the heater?

Two bodies of equal mass A and B are brought into thermal contact. Object A has a temperature of  0 °C and object B has a temperature of 100 °C. Object A has a specific heat capacity greater than object B. The thermal equilibrium temperature of the system is T.

No other exchanges of heat take place.

Which statement is correct?

Energy is provided to a solid at its melting rate of P joules per second. The rate at which the mass is melting away is α kg per second. 

What is the specific latent heat of fusion of the solid?

The peak wavelength of two lamps are compared. The first lamp has a filament in a vacuum with a temperature of 1200 K under normal working conditions. The second similar lamp is gas-filled and has a filament temperature of 2400 K.

What is an estimate for the ratio of the wavelength at which the maximum intensity of radiation is emitted by the vacuum lamp and the gas-filled lamp?

The radiation emitted from an asteroid is monitored and the following spectrum is obtained. 

Which of the following is a sensible estimate for the temperature of the asteroid. 

The sun behaves as an approximate black-body radiator with peak energy radiation occurring at wavelength 51 × 10⁻⁸ m and a power of 4 × 10²⁶ W.

What is the correct expression for the radius of the Sun?

Rigel A in the constellation of Orion is a massive blue variable star with a peak wavelength of 0.25 μm. 

Which of the graphs shows the intensity of radiation emitted by Rigel A against the wavelength of that radiation? 

A double-glazed window filled with argon has an area of 3 m². The outdoor temperature is 8 °C and the indoor temperature 21 °C. 

What is the rate of heat loss in watts through the window?