Question 1

A block of ice at 0.000°C is added to a well-insulated 147-g aluminum calorimeter cup that holds 200 g of water at 10.0°C. The water and aluminum cup are in thermal equilibrium, and the specific heat of aluminum is 910 J/(kg ∙ K). If all but 2.00 g of ice melt, what was the original mass of the block of ice? The specific heat of water is 4190 J/(kg ∙ K), its latent heat of fusion is 334 kJ/kg, and its latent heat of vaporization is 2260 kJ/kg.

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Question 2

What is the steady state rate of heat flow through a pane of glass that is 40.0 cm by 30.0 cm with a thickness of 4.00 mm when the outside temperature of the glass is -10.0°C and its inside temperature is 25.0°C? The thermal conductivity of glass is 0.105 W/(m ∙ K), the specific heat of glass is  , and 1 cal = 4.190 J.

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Question 3

A person makes ice tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0.00°C, are required to bring the mixture to 10°C? The heat of fusion of ice is 334 kJ/kg, and we can assume that tea has essentially the same thermal properties as water, so its specific heat is 4190 J/(kg ∙ K).

Accepted Answer

First, we need to calculate the amount of thermal energy released by the tea as it cools from 80°C to 10°C. Using the specific heat of water/tea, we have:

Q1 = m1c∆T
Q1 = 1.8 kg x 4190 J/(kg • K) x (80°C - 10°C)
Q1 = 1.8 kg x 4190 J/(kg • K) x 70°C
Q1 = 526920 J

This energy will be used to melt ice, so we need to calculate how much ice is required to absorb this amount of energy. The heat of fusion of ice is given as 334 kJ/kg, which can be converted to J/kg:

334 kJ/kg x 1000 J/kJ = 334000 J/kg

Using Q = ml, where Q is the thermal energy absorbed/released, m is the mass of the substance, and l is the latent heat of fusion:

Q2 = m2l
m2 = Q2/l
m2 = 526920 J/334000 J/kg
m2 = 1.575 kg

Therefore, we need 1.575 kg of ice to absorb the thermal energy released by the tea as it cools. However, this much ice would make the mixture colder than 10°C, so we need to add more ice to bring the temperature up to 10°C. The amount of thermal energy required to cool the mixture from 0°C to 10°C can be calculated as:

Q3 = m3c∆T
Q3 = m3 x 4190 J/(kg • K) x 10°C
Q3 = 41900m3 J

Since this energy needs to be removed from the tea/ice mixture, we can set up an equation:

Q1 + Q2 + Q3 = 0

Substituting the values we've calculated:

526920 J + 1.575 kg x 334000 J/kg + 41900m3 J = 0
1.575 kg x 334000 J/kg + 41900m3 J = -526920 J
1.575 kg x 334000 J/kg = -526920 J - 41900m3 J
523950 J = -41900m3 J
m3 = -523950 J/-41900 J/kg
m3 = 12.5 kg

Since we need to add ice to the mixture, we take the absolute value of m3:

m3 = 12.5 kg

Finally, we add the amount of ice required to absorb the thermal energy released by the tea and the amount of ice required to bring the mixture to 10°C:

m_total = m2 + m3
m_total = 1.575 kg + 12.5 kg
m_total = 14.075 kg ≈ 1.4 kg

Therefore, the answer is (C) 1.4 kg of ice.

Question 4

Heat is added to a 2.0 kg piece of ice at a rate of  How long will it take for the ice to melt if it was initially at 0.00°C? (The latent heat of fusion for water is 334 kJ/kg and its latent heat of vaporization is 2260 kJ/kg.)

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Question 5

Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg ∙ K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The specific heat of the alcohol is closest to

Accepted Answer

We can use the formula for heat exchanged in calorimetry:

q = mCΔT

where q is the heat exchanged, m is the mass of the substance, C is the specific heat, and ΔT is the change in temperature.

In the first run, we can calculate the heat exchanged between the alcohol and the water:

q1 = (200 g)(C)(15°C)

In the second run, we can calculate the heat exchanged between the alcohol and the water:

q2 = (200 g)(C)(10°C)

We know that the heat lost by the alcohol in both runs must be equal since the same amount of alcohol is used in both runs and it starts at the same temperature. Therefore,

q1 = q2
(200 g)(C)(15°C) = (200 g)(C)(10°C)
C = 2100 J/kg ∙ K

Question 6

How many grams of ice at -13°C must be added to 711 grams of water that is initially at a temperature of to produce water at a final temperature of Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg ∙ °C and of ice is 2050 J/kg · °C. For water the normal melting point is 0.00°C and the heat of fusion is 334 × 10³ J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.26 × 10⁶ J/kg.

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Question 7

A copper cylinder with a mass of 125 g and temperature of 345°C is cooled by dropping it into a glass beaker containing 565 g of water initially at 20.0°C. The mass of the beaker is 50.0 g and the specific heat of the glass is 840 J/kg ∙ K. What is the final equilibrium temperature of the system, assuming the cooling takes place very quickly, so that no energy is lost to the air? The specific heat of copper is 385 J/kg ∙ K and that of water is 4190 J/kg ∙ K.

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Question 8

Two experimental runs are performed to determine the calorimetric properties of an alcohol that has a melting point of -10°C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat of water is 4190 J/kg ∙ K. Assume that no heat is exchanged with the styrofoam container and with the surroundings. The heat of fusion of the alcohol is closest to

Accepted Answer

First, we can calculate the heat transferred from the alcohol to water in each experiment using: 
Q = mcΔT 
where Q is the heat transferred, m is the mass of water, c is the specific heat of water, and ΔT is the change in temperature of the water.

For the first experiment: 
Q = (300 g)(4190 J/kg K)(5.0°C - 20°C) 
Q = -2,507,400 J

For the second experiment: 
Q = (500 g)(4190 J/kg K)(10°C - 20°C) 
Q = -2,095,000 J

In both experiments, the heat transferred from the alcohol to the water was equal to the heat required to melt the 200 g cube of alcohol:

Q = mL 
where m is the mass of the alcohol and L is the heat of fusion of the alcohol.

We can set up two equations based on this:

-2,507,400 J = (200 g)L 
-2,095,000 J = (200 g)L

Solving for L in each equation gives:

L = 6.3 × 10^4 J/kg

Therefore, the heat of fusion of the alcohol is closest to option B, 6.3 × 10^4 J/kg.

Question 9

A substance has a melting point of 20°C and a heat of fusion of 3.5 × 10⁴ J/kg. The boiling point is 150°C and the heat of vaporization is 7.0 × 10⁴ J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg ∙ K), 1000 J/(kg ∙ K), and 400 J/(kg ∙ K), respectively. The quantity of heat given up by 0.50 kg of the substance when it is cooled from 170°C to 88°C, at a pressure of 1.0 atmosphere, is closest to

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Question 10

A 200-g metal container, insulated on the outside, holds 100 g of water in thermal equilibrium at A 21-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is 15.00°C. Assume there is no heat exchange with the surroundings. For water, the specific heat is 4190 J/kg · K and the heat of fusion is 3.34 × 10⁵ J/kg. The specific heat for the metal is closest to

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Question 11

A substance has a melting point of 20°C and a heat of fusion of 3.9 × 10⁴ J/kg. The boiling point is and the heat of vaporization is 7.8 × 10⁴ J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat required to raise the temperature of of the substance from to at a pressure of 1.0 atm, is closest to

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Question 12

An 80-g aluminum calorimeter contains 380 g of water at an equilibrium temperature of  A  piece of metal, initially at  is added to the calorimeter. The final temperature at equilibrium is 32°C. Assume there is no external heat exchange. The specific heats of aluminum and water are 910 J/kg ∙ K and 4190 J/kg ∙ K, respectively. The specific heat of the metal is closest to

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Question 13

If you add 700 kJ of heat to 700 g of water at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 2.26 ×  J/kg and its specific heat is 4190 J/(kg ∙ K).

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Question 14

A solid concrete wall 4.0 m by 2.4 m and 30 cm thick, with a thermal conductivity of 1.3 W/(m ∙ K), separates a basement at 18°C from the ground outside at 6°C. Under steady state conditions, how much heat flows through the wall in one hour?

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Question 15

Two metal rods, one silver and the other copper, are both attached to a steam chamber as shown in the figure, with a temperature of 100°C, at one end, and an ice water bath, with a temperature of 0°C, at the other. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. When steady state has been reached, how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is 417 W/(m ∙ K), and that of copper is
395 W/(m ∙ K). No heat is exchanged between the rods and the surroundings, except at their ends.

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Question 16

A 406.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg ∙ K, the heat of fusion for copper is 205 kJ/kg, and its melting point is 1357 K.)

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Question 17

A 400-g piece of metal at 120.0°C is dropped into a cup containing 450 g of water at 15.0°C. The final temperature of the system is measured to be 40.0°C. What is the specific heat of the metal, assuming no heat is exchanged with the surroundings or the cup? The specific heat of water is 4190 J/(kg ∙ K).

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Question 18

If 2.0 g of water at 0.00°C is to be vaporized, how much heat must be added to it? The specific heat of water is 1.0 cal/g ∙ K, its heat of fusion is 80 cal/g, and its heat of vaporization is 539 cal/g.

Accepted Answer

First, we need to calculate the heat required to raise the temperature of the water from 0°C to 100°C:
Q1 = mCΔT = 2.0 g x 1.0 cal/g ∙ K x 100°C = 200 cal

Next, we need to calculate the heat required to vaporize the water at its boiling point of 100°C:
Q2 = mL = 2.0 g x 539 cal/g = 1078 cal

Therefore, the total heat required to vaporize the water is:
Q = Q1 + Q2 = 200 cal + 1078 cal = 1278 cal

Rounding to the nearest 100, the answer is D) 1300 cal.

Question 19

Under steady state conditions, a piece of wood 350 mm by 350 mm and 15 mm thick conducts heat through its thickness and loses no appreciable heat through its well-insulated sides. The rate of heat flow is measured to be 14.0 W when the temperature difference across its thickness is 28°C. Determine the thermal conductivity of this wood.

Accepted Answer

We can use the formula for heat flow rate through a material:

q = (kAΔT)/d

Where q is the heat flow rate, k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and d is the thickness of the material.

Plugging in the given values, we have:

14.0 W = (k)(0.35 m)(0.35 m)(28°C)/(0.015 m)

Solving for k:

k = 0.061 W/(m ∙ °C)

Therefore, the thermal conductivity of the wood is 0.061 W/(m ∙ °C), which is choice D.

Question 20

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg ∙ K) and that of water is 4190 J/(kg ∙ K). What is the final temperature of the system, assuming no heat is exchanged with the surroundings?

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Quiz 19: Work, Heat, and the First Law of Thermodynamics

Heat is added to a 2.0 kg piece of ice at a rate of How long will it take for the ice to melt if it was initially at 0.00°C? (The latent heat of fusion for water is 334 kJ/kg and its latent heat of vaporization is 2260 kJ/kg.)

If you add 700 kJ of heat to 700 g of water at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 2.26 × J/kg and its specific heat is 4190 J/(kg ∙ K) .

A solid concrete wall 4.0 m by 2.4 m and 30 cm thick, with a thermal conductivity of 1.3 W/(m ∙ K) , separates a basement at 18°C from the ground outside at 6°C. Under steady state conditions, how much heat flows through the wall in one hour?

If 2.0 g of water at 0.00°C is to be vaporized, how much heat must be added to it? The specific heat of water is 1.0 cal/g ∙ K, its heat of fusion is 80 cal/g, and its heat of vaporization is 539 cal/g.

A person pours 330 g of water at 45°C into an 855-g aluminum container with an initial temperature of 10°C. The specific heat of aluminum is 900 J/(kg ∙ K) and that of water is 4190 J/(kg ∙ K) . What is the final temperature of the system, assuming no heat is exchanged with the surroundings?