3.1 Thermal Concepts

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 added to 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 vapourisation 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 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. 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?

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 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 4000 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?

A flask contains a mass m of a fluid. When 2000 J of heat is provided the temperature of the water and the flask increases by 10 K.

The mass of the fluid is doubled, and the experiment is repeated. This time 4500 J is required to increase the temperature by 10 K.

The specific heat capacity of the fluid is 5000 J kg^–1 K^–1.

What is the value of m?