Test: Work, Energy And Power

1. If two substances of equal mass are supplied the same amount of thermal energy and their final temperatures are different, you can assume that they have

Different heat capacities

The same volume

Different abilities to conduct heat

Different densities

Different volumes

If two substances of equal mass are supplied with the same amount of thermal energy and their final temperatures are different, it suggests that they have different heat capacities. Heat capacity is the amount of thermal energy required to raise the temperature of a substance by a certain amount. Therefore, if the substances have different final temperatures despite receiving the same amount of thermal energy, it indicates that they have different heat capacities.

Explanation

If two substances of equal mass are supplied with the same amount of thermal energy and their final temperatures are different, it suggests that they have different heat capacities. Heat capacity is the amount of thermal energy required to raise the temperature of a substance by a certain amount. Therefore, if the substances have different final temperatures despite receiving the same amount of thermal energy, it indicates that they have different heat capacities.

2. How much heat is required to raise the temperature of 40 g of water 20°C? (c_w = 4.18 ´ 10³J/kg·°C)

5.2 J

3.3 x 103 J

8.0 x 10–1 J

3.3 x 105 J

2.1 x 106 J

The correct answer is 3.3 x 103 J. This is because the amount of heat required to raise the temperature of a substance can be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. In this case, the mass of water is 40 g and the change in temperature is 20°C. The specific heat capacity of water is 4.18 ´ 103 J/kg·°C. Plugging these values into the formula, we get Q = (40 g) * (4.18 ´ 103 J/kg·°C) * (20°C) = 3.3 x 103 J.

Explanation

The correct answer is 3.3 x 103 J. This is because the amount of heat required to raise the temperature of a substance can be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. In this case, the mass of water is 40 g and the change in temperature is 20°C. The specific heat capacity of water is 4.18 ´ 103 J/kg·°C. Plugging these values into the formula, we get Q = (40 g) * (4.18 ´ 103 J/kg·°C) * (20°C) = 3.3 x 103 J.

3. The transfer of heat through a material by collision of the atoms is called

Heat transfer

Convection

Radiation

Heat exchange

Conduction

Conduction is the transfer of heat through a material by the collision of atoms. In this process, heat energy is transferred from higher temperature regions to lower temperature regions within the material. Unlike convection and radiation, which involve the transfer of heat through fluids or electromagnetic waves, conduction occurs within a solid or stationary fluid. Therefore, conduction is the correct answer for the given question.

Explanation

Conduction is the transfer of heat through a material by the collision of atoms. In this process, heat energy is transferred from higher temperature regions to lower temperature regions within the material. Unlike convection and radiation, which involve the transfer of heat through fluids or electromagnetic waves, conduction occurs within a solid or stationary fluid. Therefore, conduction is the correct answer for the given question.

4. A 50 W immersion heater is switched on for 1 minute to heat up a cup of water. How much energy is supplied to the water?

50 J

1000 J

2000 J

3000 J

0.833 J

The energy supplied to the water can be calculated using the formula: Energy = Power x Time. In this case, the power of the immersion heater is 50 W and the time it is switched on for is 1 minute. By substituting these values into the formula, we get: Energy = 50 W x 1 min = 50 J/min. Since 1 min is equivalent to 60 seconds, we can convert the energy to Joules by multiplying by 60: Energy = 50 J/min x 60 min = 3000 J. Therefore, the correct answer is 3000 J.

Explanation

The energy supplied to the water can be calculated using the formula: Energy = Power x Time. In this case, the power of the immersion heater is 50 W and the time it is switched on for is 1 minute. By substituting these values into the formula, we get: Energy = 50 W x 1 min = 50 J/min. Since 1 min is equivalent to 60 seconds, we can convert the energy to Joules by multiplying by 60: Energy = 50 J/min x 60 min = 3000 J. Therefore, the correct answer is 3000 J.

5. When water at 100 Celcius is cooled to 50 Celcius, which of the following is true?

The kinetic energy of the water molecules remains constant, while heat energy is being released to its surroundings.

The kinetic energy of the water molecules is increasing, while heat energy is being absorbed by the molecules.

Heat energy from the surroundings is being used to increase the kinetic energy of the water molecules.

The kinetic energy of the water molecules is being transferred to heat energy being released to its surroundings.

Only the kinetic energy of the particles is being increased.

When water at 100 Celsius is cooled to 50 Celsius, the kinetic energy of the water molecules decreases. This decrease in kinetic energy is transferred to the surroundings as heat energy, causing the water to cool down. Therefore, the correct answer is that the kinetic energy of the water molecules is being transferred to heat energy being released to its surroundings.

Explanation

When water at 100 Celsius is cooled to 50 Celsius, the kinetic energy of the water molecules decreases. This decrease in kinetic energy is transferred to the surroundings as heat energy, causing the water to cool down. Therefore, the correct answer is that the kinetic energy of the water molecules is being transferred to heat energy being released to its surroundings.

6. In the ice ages, cave men and women didn’t have pots and pans they could set on the fire to heat water for tea. Instead, they had tightly woven waterproof bags and dropped hot rocks from the fire into the water-filled bag to heat the water. If the specific heat of water is 1 cal/g^oC and the specific heat of rock is 0.1 cal/g^oC, how many grams of rocks at 200^oC must be added to 100 grams of water to raise the water temperature from 20^oC to 80^oC?

200 g

500 g

667 g

1250 g

1470 g

In order to raise the temperature of the water from 20oC to 80oC, we need to calculate the amount of heat energy required. We can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, we calculate the heat energy required for the water:
Q_water = (100 g)(1 cal/goC)(80oC - 20oC) = 6000 cal

Next, we calculate the heat energy that can be provided by the rocks:
Q_rocks = (m)(0.1 cal/goC)(200oC - 80oC)

Since the heat energy provided by the rocks must be equal to the heat energy required by the water, we can set up the equation:
Q_rocks = Q_water

(m)(0.1 cal/goC)(200oC - 80oC) = 6000 cal

Simplifying the equation, we get:
(m)(0.1 cal/goC)(120oC) = 6000 cal

Solving for m, we find:
m = 500 g

Therefore, 500 grams of rocks at 200oC must be added to 100 grams of water to raise the water temperature from 20oC to 80oC.

Explanation

In order to raise the temperature of the water from 20oC to 80oC, we need to calculate the amount of heat energy required. We can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, we calculate the heat energy required for the water:
Q_water = (100 g)(1 cal/goC)(80oC - 20oC) = 6000 cal

Next, we calculate the heat energy that can be provided by the rocks:
Q_rocks = (m)(0.1 cal/goC)(200oC - 80oC)

Since the heat energy provided by the rocks must be equal to the heat energy required by the water, we can set up the equation:
Q_rocks = Q_water

(m)(0.1 cal/goC)(200oC - 80oC) = 6000 cal

Simplifying the equation, we get:
(m)(0.1 cal/goC)(120oC) = 6000 cal

Solving for m, we find:
m = 500 g

Therefore, 500 grams of rocks at 200oC must be added to 100 grams of water to raise the water temperature from 20oC to 80oC.

7. The fact that desert sand is very hot in the day and very cold at night is evidence that sand has a

Low specific heat capacity

High specific heat capacity

Low heat of fusion

High heat of fusion

Problem

The fact that desert sand is very hot in the day and very cold at night suggests that sand has a low specific heat capacity. Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. Sand heats up quickly during the day because it has a low specific heat capacity, meaning it requires less heat energy to increase its temperature. Similarly, it cools down rapidly at night because it releases heat quickly due to its low specific heat capacity.

Explanation

The fact that desert sand is very hot in the day and very cold at night suggests that sand has a low specific heat capacity. Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. Sand heats up quickly during the day because it has a low specific heat capacity, meaning it requires less heat energy to increase its temperature. Similarly, it cools down rapidly at night because it releases heat quickly due to its low specific heat capacity.

8. It is necessary to determine the specific heat of an unknown object. The mass of the object is 227.0 g. It is determined experimentally that it takes 16.0 J to raise the temperature 10.0^oC. Find the specific heat capacity of the object.

0.001,40 J/kg K

7.05 J/kg K

3,630,000 J/kg K

1600 J/kg K

None of the above

The specific heat capacity of an object is defined as the amount of heat energy required to raise the temperature of a unit mass of the object by 1 degree Kelvin or Celsius. In this case, the mass of the object is given as 227.0 g and it takes 16.0 J of energy to raise its temperature by 10.0oC. To find the specific heat capacity, we can use the formula: specific heat capacity = (energy)/(mass x change in temperature). Plugging in the values, we get specific heat capacity = (16.0 J)/(227.0 g x 10.0oC) = 7.05 J/kg K. Therefore, the correct answer is 7.05 J/kg K.

Explanation

The specific heat capacity of an object is defined as the amount of heat energy required to raise the temperature of a unit mass of the object by 1 degree Kelvin or Celsius. In this case, the mass of the object is given as 227.0 g and it takes 16.0 J of energy to raise its temperature by 10.0oC. To find the specific heat capacity, we can use the formula: specific heat capacity = (energy)/(mass x change in temperature). Plugging in the values, we get specific heat capacity = (16.0 J)/(227.0 g x 10.0oC) = 7.05 J/kg K. Therefore, the correct answer is 7.05 J/kg K.

9. At midnight, you walk outside. The temperature of the air has been exactly -12 Celcius for several hours. You touch a metal fence post, a block of wood, and some snow. Apply the concept of thermal equilibrium to identify the correct statement.

The fence post has the lowest temperature.

The block will have the highest temperature.

The fence post, the block of wood, and the snow will all be at a temperature of -12 Celcius.

The process of thermal equilibrium causes cold to flow from objects with low specific heat capacities.

Determining which object will have the lowest temperature is impossible without knowing the specific heat capacities.

According to the concept of thermal equilibrium, when objects are in contact with each other for a sufficient amount of time, they will reach the same temperature. In this case, since the air temperature has been -12 Celsius for several hours, the fence post, the block of wood, and the snow will all be at a temperature of -12 Celsius. Therefore, the correct statement is that the fence post, the block of wood, and the snow will all be at a temperature of -12 Celsius.

Explanation

According to the concept of thermal equilibrium, when objects are in contact with each other for a sufficient amount of time, they will reach the same temperature. In this case, since the air temperature has been -12 Celsius for several hours, the fence post, the block of wood, and the snow will all be at a temperature of -12 Celsius. Therefore, the correct statement is that the fence post, the block of wood, and the snow will all be at a temperature of -12 Celsius.

10. If a block of iron and a slice of watermelon are left in a refrigerator for a looooong period of time, compare the temperatures of both when they are immediately removed from the refrigerator.

The iron will have a colder temperature than the watermelon.

The watermelon will have a colder temperature than the iron.

The iron will feel colder because it is a good conductor of heat which is drawn from your fingers.

The iron will feel colder because it has a very high specific heat capacity.

They both feel equally cold.

The iron will feel colder because it is a good conductor of heat which is drawn from your fingers. Unlike the watermelon, which is a poor conductor of heat, the iron quickly transfers its temperature to your fingers, giving the sensation of coldness.

Explanation

The iron will feel colder because it is a good conductor of heat which is drawn from your fingers. Unlike the watermelon, which is a poor conductor of heat, the iron quickly transfers its temperature to your fingers, giving the sensation of coldness.

11. A 2000-W tennis ball machine releases 0.028-kg balls at a speed of 100 m/s in 0.20 s. The efficiency of the machine is

70%

14%

28%

1.4%

7.0%

The efficiency of a machine is calculated by dividing the useful output energy by the input energy and multiplying by 100%. In this case, the useful output energy is the kinetic energy of the tennis balls, which can be calculated using the formula 1/2 * mass * velocity^2. The input energy is the power of the machine multiplied by the time it takes to release the balls. By calculating the ratio of the two energies and multiplying by 100%, we find that the efficiency of the machine is 70%.

Explanation

The efficiency of a machine is calculated by dividing the useful output energy by the input energy and multiplying by 100%. In this case, the useful output energy is the kinetic energy of the tennis balls, which can be calculated using the formula 1/2 * mass * velocity^2. The input energy is the power of the machine multiplied by the time it takes to release the balls. By calculating the ratio of the two energies and multiplying by 100%, we find that the efficiency of the machine is 70%.

12. How long will it take a 500W microwave oven to vaporize completely a 500g block of ice that is initially at zero degree Celsius? (Lf = 334 kJ/kg; cw = 4.184 kJ/kg°C, Lv = 2257 kJ/kg) (Hint: This could be a long one, just be patient and work out the solution)

1 min

10 min

1 hour

10 hours

1 day

To calculate the time it takes for the microwave oven to vaporize the ice completely, we need to consider the energy required to heat the ice from 0°C to its melting point, melt the ice, and then heat the resulting water from 0°C to its boiling point and vaporize it.

First, we calculate the energy required to heat the ice from 0°C to its melting point using the specific heat capacity of ice (cw). The energy is given by Q = mcwΔT, where m is the mass of the ice (500g), cw is the specific heat capacity of ice (4.184 kJ/kg°C), and ΔT is the change in temperature (0°C to 0°C, so ΔT = 0). Therefore, the energy required to heat the ice is 0 kJ.

Next, we calculate the energy required to melt the ice using the latent heat of fusion (Lf). The energy is given by Q = mLf, where m is the mass of the ice (500g) and Lf is the latent heat of fusion (334 kJ/kg). Therefore, the energy required to melt the ice is 500g * 334 kJ/kg = 167,000 kJ.

Finally, we calculate the energy required to heat the resulting water from 0°C to its boiling point and vaporize it using the specific heat capacity of water (cw) and the latent heat of vaporization (Lv). The energy is given by Q = mcwΔT + mLv, where m is the mass of the water (500g), cw is the specific heat capacity of water (4.184 kJ/kg°C), ΔT is the change in temperature (0°C to 100°C, so ΔT = 100°C), and Lv is the latent heat of vaporization (2257 kJ/kg). Therefore, the energy required is 500g * 4.184 kJ/kg°C * 100°C + 500g * 2257 kJ/kg = 2,092 kJ + 1,128.5 kJ = 3,220.5 kJ.

Now, we calculate the time it takes to supply this energy using the power of the microwave oven (500W). The time is given by t = Q / P, where Q is the energy required (3,220.5 kJ) and P is the power of the

Explanation

To calculate the time it takes for the microwave oven to vaporize the ice completely, we need to consider the energy required to heat the ice from 0°C to its melting point, melt the ice, and then heat the resulting water from 0°C to its boiling point and vaporize it.

First, we calculate the energy required to heat the ice from 0°C to its melting point using the specific heat capacity of ice (cw). The energy is given by Q = mcwΔT, where m is the mass of the ice (500g), cw is the specific heat capacity of ice (4.184 kJ/kg°C), and ΔT is the change in temperature (0°C to 0°C, so ΔT = 0). Therefore, the energy required to heat the ice is 0 kJ.

Next, we calculate the energy required to melt the ice using the latent heat of fusion (Lf). The energy is given by Q = mLf, where m is the mass of the ice (500g) and Lf is the latent heat of fusion (334 kJ/kg). Therefore, the energy required to melt the ice is 500g * 334 kJ/kg = 167,000 kJ.

Finally, we calculate the energy required to heat the resulting water from 0°C to its boiling point and vaporize it using the specific heat capacity of water (cw) and the latent heat of vaporization (Lv). The energy is given by Q = mcwΔT + mLv, where m is the mass of the water (500g), cw is the specific heat capacity of water (4.184 kJ/kg°C), ΔT is the change in temperature (0°C to 100°C, so ΔT = 100°C), and Lv is the latent heat of vaporization (2257 kJ/kg). Therefore, the energy required is 500g * 4.184 kJ/kg°C * 100°C + 500g * 2257 kJ/kg = 2,092 kJ + 1,128.5 kJ = 3,220.5 kJ.

Now, we calculate the time it takes to supply this energy using the power of the microwave oven (500W). The time is given by t = Q / P, where Q is the energy required (3,220.5 kJ) and P is the power of the

13. A 100-gram ice cube at 0^oC is dropped into 100 grams of water at 20^oC. When the ice melts, what will be temperature of the water? The latent heat of fusion for water is 333000 J/kg and the specific heat capacity of water is 4186 J/kg^oC. (Hint: First, determine the amount of ice the water would be able to melt.)

1.2 Celcius

1.8 Celcius

2.0 Celcius

11.3 Celcius

0 Celcius (not all the ice melts)

When the ice cube is dropped into the water, heat will be transferred from the water to the ice cube in order to melt it. The amount of heat transferred can be calculated using the equation Q = m * L, where Q is the heat transferred, m is the mass of the ice, and L is the latent heat of fusion. In this case, the mass of the ice is 100 grams and the latent heat of fusion is 333000 J/kg. Therefore, the total heat transferred is 33300 J. This amount of heat is not enough to melt all the ice, as the specific heat capacity of water is 4186 J/kgoC. Therefore, the temperature of the water will remain at 0oC until all the ice has melted.

Explanation

When the ice cube is dropped into the water, heat will be transferred from the water to the ice cube in order to melt it. The amount of heat transferred can be calculated using the equation Q = m * L, where Q is the heat transferred, m is the mass of the ice, and L is the latent heat of fusion. In this case, the mass of the ice is 100 grams and the latent heat of fusion is 333000 J/kg. Therefore, the total heat transferred is 33300 J. This amount of heat is not enough to melt all the ice, as the specific heat capacity of water is 4186 J/kgoC. Therefore, the temperature of the water will remain at 0oC until all the ice has melted.

14. A 621.0-g iron meteor impacts the earth at a speed of 1922.0 m/s. If its energy is entirely converted to heat of the meteorite, what will the resultant temperature rise be? (The specific heat for iron is 447 J/kg°C.)

6.30 Celcius

63 Celcius

16300 Celcius

2430 Celcius

4000 Celcius

When the iron meteor impacts the earth, its kinetic energy is converted entirely into heat energy. We can use the equation for kinetic energy (KE) to find the amount of heat energy produced. KE = 1/2 * mass * velocity^2. Plugging in the given values, we get KE = 1/2 * 0.621 kg * (1922 m/s)^2 = 1136.5 kJ. To find the temperature rise, we can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the temperature change. Rearranging the equation, we can solve for ΔT = Q / (mc). Plugging in the values, we get ΔT = (1136.5 kJ) / (0.621 kg * 447 J/kg°C) = 4057.6 °C. Rounding to the nearest whole number, the resultant temperature rise is 4000 °C.

Explanation

When the iron meteor impacts the earth, its kinetic energy is converted entirely into heat energy. We can use the equation for kinetic energy (KE) to find the amount of heat energy produced. KE = 1/2 * mass * velocity^2. Plugging in the given values, we get KE = 1/2 * 0.621 kg * (1922 m/s)^2 = 1136.5 kJ. To find the temperature rise, we can use the equation Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the temperature change. Rearranging the equation, we can solve for ΔT = Q / (mc). Plugging in the values, we get ΔT = (1136.5 kJ) / (0.621 kg * 447 J/kg°C) = 4057.6 °C. Rounding to the nearest whole number, the resultant temperature rise is 4000 °C.

15. A blacksmith heats a 1.1kg iron horseshoe to 550 degree Celsius, then plunges it into a bucket containing 15 kg of water at 20 degree Celsius. What is the final temperature? Assume that the transfer of heat is 100% efficient. (specific heat water = 1 cal/g^oC; iron = 0.107 cal/g^oC).

42 Celcius

15 Celcius

48 Celcius

96 Celcius

99 Celcius

When the hot horseshoe is plunged into the bucket of water, heat is transferred from the horseshoe to the water until they reach thermal equilibrium. This means that the heat lost by the horseshoe is equal to the heat gained by the water. We can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.

For the horseshoe, the heat lost is Q = mcΔT = (1.1 kg)(0.107 cal/goC)(550 - T), where T is the final temperature in Celsius.

For the water, the heat gained is Q = mcΔT = (15 kg)(1 cal/goC)(T - 20), where T is the final temperature in Celsius.

Since the transfer of heat is 100% efficient, the heat lost by the horseshoe is equal to the heat gained by the water. Setting the two equations equal to each other and solving for T gives us T = 42°C.

Explanation

When the hot horseshoe is plunged into the bucket of water, heat is transferred from the horseshoe to the water until they reach thermal equilibrium. This means that the heat lost by the horseshoe is equal to the heat gained by the water. We can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.

For the horseshoe, the heat lost is Q = mcΔT = (1.1 kg)(0.107 cal/goC)(550 - T), where T is the final temperature in Celsius.

For the water, the heat gained is Q = mcΔT = (15 kg)(1 cal/goC)(T - 20), where T is the final temperature in Celsius.

Since the transfer of heat is 100% efficient, the heat lost by the horseshoe is equal to the heat gained by the water. Setting the two equations equal to each other and solving for T gives us T = 42°C.