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physics A-Level Physics

Solved problems for the chapter:

Specific Heat Capacity

View the theory »

Heat and Temperature

1. Internal energy

2. Thermodynamic variables

2.1. Temperature measurement

3. Heat and temperature

3.1. What is heat?

3.2. Relationship between heat and temperature

3.3. Specific heat capacity and heat capacity

4. Energy theorem

5. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:specific_heat_capacity/4267/

Example 1.

How much heat is needed to raise the temperature of the air in an apartment from to if the area of the apartment is and the height is 2.6 m.

(Specific heat capacity of the air = , density of air = ).

Example 2.

1 l of hot water with the initial temperature is poured into a bottle and a thermos. After one hour, the temperatures in both vessels are measured again and the water in the thermos measures while that of the bottle measures .

How much heat does the water in each of the bottle and thermos emit?
The heat flow rate of the bottle is how many times that of the thermos?

The specific heat of the water is .

The average rate of flow of heat through the walls of a house is 4 kW. When the walls are additionally thermally insulated with a layer of styrofoam, the heat flow rate is reduced to 1 kW. How much heat per month do we need to heat the house if the walls of the house are not insulated and how much if we insulate them? What percentage of heat energy can be saved by additional insulation?

A 10 kg iron sphere is initially heated to and then cooled slowly. The graph below shows how its temperature changes over time. What is the rate of flow of heat from the sphere after the first 40 minutes of cooling?

The specific heat of iron is .

Determine whether each of the statements is correct:

Heat flow rate transfers heat through matter.
Heat current always flows from colder substance to warmer.
The greater the heat flow rate, the more heat passes through the substance in the shortest possible time.
The unit for heat flow rate is Joule per second (J / s) or watt (W).
The heat flow rate does not depend on the substance through which the heat passes.
The heat flow rate is independent of the body shape through which the heat passes.
Fluffy or woollen clothing reduces heat emitted by the body.

A power transfers heat during . In what time in terms of time does a power of transfer heat, ?

For how long does a power of 80 W transfer heat of 2000 J?

2 l of water with an initial temperature of is heated on a hob. The water temperature changes over time as shown in the graph below. What is the heat flow rate from 0 to 10 minutes? What is it like in 10 to 15 minutes? The power of the heater is not changed during the experiment.

The specific heat of the water is .

Heat with power of 100 W flows through a body. How does the heat received by the body change in the first 50 seconds? Draw a graph of heat versus time.

10.

How many times does the heat flow rate increase if twice as much heat is transferred in half time?

11.

We are heating two bodies. The first is made of iron and the second of aluminium. The masses of both bodies are equal. What should be the ratio of the heat flow rate (power) of the bodies in order for them to heat up at the same rate? This means that they will have the same temperature change in the same observed time.

The specific heat of iron is and that of aluminium is .

12.

At heat flow rate , heat quantity is transferred to a body in time . After what time, in terms of , is 6 times the heat quantity transferred to the same body if the heat flow rate is doubled?

13.

We have the same substance in two containers. The mass of the substance in the first container is twice the mass of the substance in the second container. The initial temperatures in both containers are the same. The substances are heated so that the temperatures rise evenly. After a certain time, the substance in the first container is heated by 30 K and the one in the second container by 60 K. Find the ratio of the heat flow rates (power) of the substances in both containers.

14.

The graph of heat quantity against the time for two values of heat flow rate is given. The red line in the graph represents the heat flow rate and the blue, . Calculate the values of the heat flow rate on both lines. Which is bigger?

15.

We have equal amount of the same substance in two containers. The initial temperatures of both substances are the same. The substances are heated so that the temperatures rise evenly. After a certain time, the temperature of the first substance rises by 40 K and that of the second substance by 60k. Find the ratio of the heat flow rates of the substances in both vessels.

16.

With a power of 760 W, a 1kg mass of copper is heated. How does the temperature of the copper change in the period from 0 to 50 s if the initial temperature of the copper is ? Draw the graph.

The specific heat of copper is .

17.

Bronze is an alloy of copper (80 %) and tin (20 %). If the specific heat capacity of copper and tin are 385 J / kg K and 228 J / kg K respectively, calculate the heat capacity of 6 kg of bronze.

18.

An electric water heater has a volume of .

How much electrical energy is received if the temperature of the water rises from to ?
Write the energy equation for the water in the electric heater.
What is the electrical energy finally converted into?

19.

An electric cooker consumes 800 kJ of electrical energy to heat 1 litre of water by 90 K. Write the energy equation and calculate the value of each variable in the equation.

20.

Water at a temperature of 4 °C is placed in a freezer with a capacity factor of 2. How long does it take the freezer to freeze 1.5 litres of water if the input power is 1 kW?

The specific heat of fusion of water is , the specific heat capacity of water is , and the density of water is .

21.

In a home, we have a central heating stove with an efficiency of 38 %. The stove uses heating oil with a specific heat of combustion of . How many litres of heating oil do we use if we heat 1 hectolitre of water from 25 °C to 100 °C? The density of the heating oil is and the specific heat capacity of water is .