Conservation of energy answers

Conservation of Energy

(Use g = 9.8 N kg^-1)

1. A waterfall is 120 m high. If 75 % of the potential energy available is converted into heat energy, find the difference in temperature between the top and bottom of the fall. The specific heat capacity of water is 4200 J kg^-1 K^-1.                                       .21K

2. A lead bullet moving at 210 m s^-1 is brought to rest on hitting a target. If 60 % of its energy is converted into heat energy, find the rise in temperature of the bullet. The specific heat capacity of lead is

140 J kg^-1 K^-1.                                   94.5K

3. A lump of lead falls to the ground and its temperature rises by 1.4 °C. If all the potential energy is converted into heat energy, find the height fallen, if the specific heat capacity of lead is 140 J kg^-1 K^-1.                20m

4. If 60 % of the potential energy available in a waterfall is converted into heat energy, find the height of the waterfall when the temperature difference between the top and the bottom of the fall is 0.21 °C. (The specific heat capacity of water = 4200 J kg^-1 K^-1.)                  150m

5. A paddle wheel is made to rotate inside a calorimeter containing water by a mass of 12 kg falling through a height of 2 m. The total heat capacity of the calorimeter and its contents is 800 J K^-1. Find the rise in temperature of the water.                        .294K

6. A car of mass 800 kg is moving at 108 km h^-1. What heat energy is produced in the brake drums when it is brought to rest by the brakes?             360 kJ

7. On entering the earth's atmosphere the velocity of a meteorite of mass 6 kg is reduced rapidly from 300 m s^-1 to 100 m s^-1. How much heat energy is produced?                  240 kJ

8. A lead bullet moving at 70 m s^-1 is brought to rest on hitting a target. If 80% of its energy is converted into heat energy, find the rise in temperature. (The specific heat capacity of lead = 140 J kg^-1 K^-1.)                  14K

9. A lead bullet at 40.5 °C before impact just melts when it hits a target without rebounding. If all the energy of the bullet is converted into heat energy, find the velocity of the bullet. (The specific heat capacity of lead = 140 J kg^-1 K^-1. The melting point of lead = 328 °C. The specific latent heat of fusion of lead = 21 000 J kg^-1.)                  350ms^-1

Latent Heat Answers

Latent Heat

Latent Heat of fusion of ice = 3.36 x 10⁵ J kg^-1

Latent Heat of vaporization of water = 2.25 x 10⁶ J kg^-1

Specific heat capacity of water = 4200 J kg^-1 K^-1

1. How much heat energy is needed to change 0.010 kg of water at 20^oC to steam at 100^oC?                    25860J
2. How much heat energy is needed to change 0.020 kg of ice at 0°C into steam at 100°C?           60 120J  
3. How much heat energy is needed to melt 0.010 kg of ice at 0^o C and then heat the water formed to 20^o C? 4200j
4. What mass of ice at 0 °C is needed to cool 0.086 kg of water from      54 °C to 6 °C?                     .048kg
5. When a kettle boils a space can be seen between the spout and the so called `cloud of steam'. If your finger were placed in the space a much more serious scald would result than if it were placed in the `cloud of steam'. Explain why, and criticize the expression `cloud of steam'.
6. A heating coil takes 14 min to heat 0.20 kg of water from 20 °C to boiling point. How much longer will it take to boil away 0.02 kg of the boiling water?     562.5s
7. A 1 kW immersion heater takes 225 s to boil away 0.1 kg of water at 100 °C. Find the specific latent heat of vaporization of water.                     2.25x 10⁶ J kg^-1
8. How long will it take an immersion heater of power 500 W to boil away a mixture of 0.05 kg of water and 0.02 kg of ice initially at 0 °C? 387 s
9. A mixture of ice and water at 0 °C contains 0.060 kg of ice. A 750 W immersion heater takes 26.8 s to melt all the ice. Deduce a value for the specific latent heat of fusion of ice.        336000J kg^-1
10. A mixture of ice and water at 0 °C has a total mass of 1 kg, and con­tains 0.5 kg of ice. An immersion heater melts all the ice in 168 s, and then needs a further 84 s to heat the mixture to 20 ^°C. Find the specific latent heat of fusion of ice.            336000 Jkg^-1
11. A vessel of heat capacity 115 J K^-1 contains 0.30 kg of water and 0.20 kg of ice at 0 °C. An immersion heater takes 134.4 s to melt the ice and a further 88.6 s to heat the vessel and its contents to 20 °C. Find the specific latent heat of fusion of ice. 336000 Jkg^-1
12. A heating coil takes 115 s to heat 0.05 kg of a liquid from 20 °C to its boiling-point of 80 °C. It needs a further 340 s to boil away 0.02 kg of the liquid. If the specific heat capacity of the liquid is 2300 J kg^-1 K^-1, find its specific latent heat of vaporization. 1.02 x 10⁶ Jkg^-1

 

Specific Heat Capacity Answers

Specific Heat Capacity

Data

Use the following for Specific Heat capacities

Substance	Specific Heat Capacity c	Units
Water	4200	J kg-1 K-1
Copper	380	J kg-1 K-1
Methylated Spirit	2500	J kg-1 K-1
Turpentine	1800	J kg-1 K-1

Notes

• The heat capacity of an object is the heat required to raise the all of the object’s temperature by 1K
• When heating a liquid you have to heat the vessel that it is in as well.
• When an object at high temperature is dropped into a liquid at low temperature there is a net heat flow from the high temperature object to the low temperature object until they are both at the same temperature.
• Unless you state “Ignoring heat losses” in each question you will lose a mark!

1 Find the quantity of heat needed to heat 0.50 kg of copper from 20^oC to 50 °C.              5700J

2 When 0.25 kg of ice are heated from -10 °C to -2 °C the heat supplied is 4200 J. Find the specific heat capacity of ice.                      2100 Jkg^-1K^-1

3 A vessel of heat capacity 30 J K^-1 contains 0.30 kg of water at 10 °C. When heated by a Bunsen burner for 5 min the temperature rises to 90 °C. At what rate does the Bunsen supply heat energy?     344W

4 A piece of iron of mass 0.20 kg is heated to 100 °C and dropped into 0.15 kg of water at 20 °C. If the temperature of the mixture is 30 °C, find a value for the specific heat capacity of iron.     450 Jkg^-1K^-1

5 A piece of iron of mass 0.05 kg is heated in a flame and then quickly transferred to a calorimeter of mass 0.05 kg and specific heat capacity 360 J kg^-1 K^-1 containing 0.18 kg of water at 18 °C. If the temperature of the water rises to 43 °C, find the temperature of the flame. The specific heat capacity of the iron is 450 J kg^-1 K^-1.                 903 ^oC

6 Which would result in the more serious burn if dropped onto your outstretched hand a white-hot spark from a firework, or a lump of red-hot iron? Explain your answer.

The white hot spark has a higher temperature than the lump of iron

The lump of iron has a greater mass than the white hot spark

They both have the same specific heat capacity.

Lump of iron has greater store of heat energy

The rate of heat transfer from the white hot spark will be greater for the spark than the lump of iron.

A greater quantity of heat will be transferred from the iron

Causing more serious skin damage.