Deck 20: The First Law of Thermodynamics

Question 1

A 300-g glass thermometer initially at 25°C is put into 200 cm³ of hot water at 95°C.Find the final temperature (in °C)of the thermometer,assuming no heat flows to the surroundings.(The specific heat of glass is 0.2 cal/g⋅°C. )

A)52
B)68
C)89
D)79
E)36

Answer 1

79

Question 2

Gas in a container increases its pressure from 1 atm to 3 atm while keeping its volume constant.Find the work done (in J)by the gas if the volume is 5 liters.

A)0
B)3
C)5
D)15
E)15 × 10²

Answer 2

0

Question 3

The R value of fiberglass batting,3.5 inches thick,is 11 ft²⋅°F⋅h/BTU.What is the thermal conductivity (in BTU/ft⋅°F⋅s)?

A)7.4 × 10−⁶
B)2.7 × 10−²
C)8.9 × 10−⁵
D)1.4 × 10−⁴
E)3.6 × 10−³

Answer 3

7.4 × 10−⁶

Question 4

A 5-gallon container of water (approximately 20 kg)having a temperature of 212°F is added to a 50-gallon tub (approximately 200 kg)of water having a temperature of 50°F.What is the final equilibrium temperature (in °C)of the mixture?

A)54
B)36
C)18
D)66
E)14

Question 5

A child has a temperature of 101°F.If her total cross-sectional area is 2 m²,find the energy lost each second (in W)due to radiation,assuming the emissivity is 1.(Assume the room temperature is 70°F. )

A)217
B)180
C)90
D)68
E)850

Question 6

A cup of coffee is enclosed on all sides in an insulated container 1/2 cm thick in the shape of a cube 10 cm on a side.The temperature of the coffee is 95°C,and the temperature of the surroundings is 21°C.Find the rate of heat loss (in J/s)due to conduction if the thermal conductivity of the cup is 2 × 10−⁴ cal/s⋅cm⋅°C.

A)62
B)74
C)230
D)160
E)12

Question 7

How much heat (in kcal)must be removed to make ice at −10°C from 2 kg of water at 20°C? (The specific heat of ice is 0.50 cal/g⋅°C. )

A)190
B)200
C)240
D)210
E)50

Question 8

A 5-kg piece of lead (specific heat 0.03 cal/g⋅°C)having a temperature of 80°C is added to 500 g of water having a temperature of 20°C.What is the final equilibrium temperature (in °C)of the system?

A)79
B)26
C)54
D)34
E)20

Question 9

How many calories of heat are required to raise the temperature of 4 kg of water from 50°F to the boiling point?

A)6.5 × 10⁵
B)3.6 × 10⁵
C)15 × 10⁵
D)360
E)4 × 10⁴

Question 10

Determine the heat capacity (in calories/°C)of a lake containing one million gallons (approximately 4 million kilograms)of water at 15°C.

A)4 × 10⁶
B)4 × 10⁹
C)4 × 10³
D)1 × 10³
E)4 × 10²

Question 11

A super-insulated house is at a temperature of 20°C.The temperature outside is 0°C.The surface area of the house is 200 m²,and the emissivity is 1.Approximately how much energy is radiated (in W)per second?

A)20 000
B)2 000
C)200
D)2
E)0.2

Question 12

In an adiabatic free expansion

A)no heat is transferred between a system and its surroundings.
B)the pressure remains constant.
C)the temperature remains constant.
D)the volume remains constant.
E)the process is reversible.

Question 13

A wall is constructed of a 2 inch layer of fiberglass board (R = 8)and six inches of fiberglass batting (R = 19).If the temperature on the outside surface of the fiberglass board is 50°F and the temperature on the inside surface of the fiberglass batting is 68°F,what is the temperature (in °F)at the interface? (The units of R are ft²⋅°F⋅h/BTU. )

A)62
B)58
C)55
D)65
E)52

Question 14

The work done in the expansion from an initial to a final state

A)is the area under the curve of a PV diagram.
B)depends only on the end point.
C)is independent of the path.
D)is the slope of a PV curve.
E)equals P(V_F − V_i).

Question 15

A 5-g coin is dropped from a 300-m building.If it reaches a terminal velocity of 45 m/s,and the rest of the energy is converted to heating the coin,what is the change in temperature (in °C)of the coin? (The specific heat of copper is 387 J/kg⋅°C. )

A)9
B)2
C)5
D)21
E)0.5

Question 16

How much heat (in kilocalories)is needed to convert 1.00 kg of ice at 0°C into steam at 100°C?

A)23.9
B)79.6
C)564
D)643
E)720

Question 17

A 100-kg student eats a 200-Calorie doughnut.To "burn it off",he decides to climb the steps of a tall building.How high (in m)would he have to climb to expend an equivalent amount of work? (1 food Calorie = 10³ calories. )

A)273
B)623
C)418
D)854
E)8 400

Question 18

A slab of concrete and an insulating board are in thermal contact with each other.The temperatures of their outer surfaces are 68°F and 50°F.Determine the rate of heat transfer (in BTU/ft²⋅h)if the R values are 1.93 and 8.7 ft²⋅°F⋅h/BTU,respectively.

A)9.7
B)2.5
C)5.3
D)1.7
E)28

Question 19

If 25 kg of ice at 0°C is combined with 4 kg of steam at 100°C,what will be the final equilibrium temperature (in °C)of the system?

A)40
B)20
C)60
D)100
E)8

Question 20

Gas in a container expands at a constant pressure of 3 atm.Find the work done (in J)by the gas if the initial volume is 5 liters and the final volume is 10 liters.

A)0
B)150
C)15
D)1 500
E)1.5

Question 21

Which statement below regarding the First Law of Thermodynamics is most correct?

A)A system can do work externally only if its internal energy decreases.
B)The internal energy of a system that interacts with its environment must change.
C)No matter what other interactions take place,the internal energy must change if a system undergoes a heat transfer.
D)The only changes that can occur in the internal energy of a system are those produced by non-mechanical forces.
E)The internal energy of a system cannot change if the heat transferred to the system is equal to the work done by the system.

Question 22

In an isovolumetric process

A)the temperature remains constant.
B)no heat is transferred between a system and its surroundings.
C)the pressure remains constant.
D)the volume remains constant.
E)the internal energy is constant.

Question 23

In which process will the internal energy of the system NOT change?

A)An adiabatic expansion of an ideal gas.
B)An isothermal compression of an ideal gas.
C)An isobaric expansion of an ideal gas.
D)The freezing of a quantity of liquid at its melting point.
E)The evaporation of a quantity of a liquid at its boiling point.

Question 24

Two kilograms of water at 100°C is converted to steam at 1 atm.Find the change in internal energy (in J).(L_v = 2.26 × 10⁶ J/kg. )

A)2.1 × 10⁴
B)4.5 × 10⁶
C)3.4 × 10⁵
D)4.2 × 10⁶
E)2.1 × 10⁶

Question 25

If an object feels cold to the touch,the only statement that you can make that must be correct is that

A)the object has a smaller coefficient of thermal conductivity than your hand.
B)the volume of the object will increase while it is in contact with your hand.
C)the object contains less thermal energy than your hand.
D)the object is at a lower temperature than your hand.
E)the object cannot be a liquid.

Question 26

A gas expands as shown in the graph.If the heat taken in during this process is 1.02 × 10⁶ J and 1 atm = 1.01 × 10⁵ N/m²,the change in internal energy of the gas (in J)is

A)−2.42 × 10⁶
B)−1.40 × 10⁶
C)−1.02 × 10⁶
D)1.02 × 10⁶
E)1.40 × 10⁶

Question 27

Water at room temperature,20°C,is pumped into a reactor core where it is converted to steam at 200°C.How much heat (in J)is transferred to each kilogram of water in this process? (c_steam = 2 010 J/kg⋅°C;L_steam = 2.26 × 10³ J/g;1 cal = 4.186 J. )

A)3.35 × 10⁵
B)7.53 × 10⁵
C)2.67 × 10⁶
D)2.80 × 10⁶
E)3.01 × 10⁶

Question 28

A gas expands from A to B as shown in the graph.Calculate the work (in joules)done by the gas.(1 atm= 1.01 × 10⁵ N/m². )

A)12
B)24
C)1.21 × 10⁶
D)2.42 × 10⁶
E)3.64 × 10⁶

Question 29

In an isothermal process

A)the volume remains constant.
B)the temperature remains constant.
C)no heat is transferred between a system and its surroundings.
D)the pressure remains constant.
E)the internal energy is not constant.

Question 30

For an astronaut working outside a spaceship,the greatest loss of heat would occur by means of

A)conduction.
B)convection.
C)radiation.
D)conduction and convection.
E)conduction and radiation.

Question 31

Five moles of an ideal gas expands isothermally at 100°C to five times its initial volume.Find the heat flow into the system.

A)2.5 × 10⁴ J
B)1.1 × 10⁴ J
C)6.7 × 10³ J
D)2.9 × 10³ J
E)7.0 × 10² J

Question 32

Determine the work done by 5 moles of an ideal gas that is kept at 100°C in an expansion from 1 liter to 5 liters.

A)2.5 × 10⁴ J
B)1.1 × 10⁴ J
C)6.7 × 10³ J
D)2.9 × 10³ J
E)8.4 × 10³ J

Question 33

One gram of water is heated from 0°C to 100°C at a constant pressure of 1 atm.Determine the approximate change in internal energy (in cal)of the water.

A)160
B)130
C)100
D)180
E)50

Question 34

Two kilograms of water at 100°C is converted to steam at 1 atm.Find the work done (in J).(The density of steam at 100°C is 0.598 kg/m³. )

A)3.4 × 10⁵
B)1.2 × 10⁵
C)4.6 × 10⁴
D)2.1 × 10⁴
E)3.4 × 10⁴

Question 35

Which of the following statements is correct?

A)You only need to know the amount of thermal energy a body contains to calculate its temperature.
B)The temperature of a body is directly proportional to the amount of work the body has performed.
C)The quantity of thermal energy exchanged by two bodies in contact is inversely proportional to the difference in their temperatures.
D)The quantity of thermal energy exchanged by two bodies in contact is directly proportional to the difference in their temperatures.
E)Different amounts of thermal energy are transferred between two bodies in contact if different temperature scales are used to measure the temperature difference between the bodies.

Question 36

An 8 000-kg aluminum flagpole 100-m long is heated by the sun from a temperature of 10°C to 20°C.Find the work done (in J)by the aluminum if the linear expansion coefficient is 24 × 10−⁶ (°C)−¹.(The density of aluminum is 2.7 × 10³ kg/m³ and 1 atm = 1.0 × 10⁵ N/m². )

A)287
B)425
C)213
D)710
E)626

Question 37

An 8 000-kg aluminum flagpole 100-m long is heated by the sun from a temperature of 10°C to 20°C.Find the heat transferred (in J)to the aluminum if the specific heat of aluminum is 0.215 cal/g⋅°C.

A)7.2 × 10⁵
B)7.2 × 10⁷
C)7.2 × 10³
D)7.2 × 10¹
E)7.2 × 10²

Question 38

In an isobaric process

A)the volume remains constant.
B)the temperature remains constant.
C)the pressure remains constant.
D)no heat is transferred between a system and its surroundings.
E)the internal energy is constant.

Question 39

How much heat,in joules,is required to convert 1.00 kg of ice at 0°C into steam at 100°C? (L_ice = 333 J/g;L_steam = 2.26 × 10³ J/g. )

A)3.35 × 10⁵
B)4.19 × 10⁵
C)2.36 × 10⁶
D)2.69 × 10⁶
E)3.01 × 10⁶

Question 40

An 8 000-kg aluminum flagpole 100-m high is heated by the sun from a temperature of 10°C to 20°C.Find the increase in internal energy (in J)of the aluminum.(The coefficient of linear expansion is 24 × 10−⁶ (°C)−¹,the density is 2.7 × 10³ kg/m³,and the specific heat of aluminum is 0.215 cal/g⋅°C. )

A)7.2 × 10⁵
B)7.2 × 10⁷
C)7.2 × 10³
D)7.2 × 10¹
E)7.2 × 10²

Question 41

The Earth intercepts 1.27 × 10¹⁷ W of radiant energy from the Sun.Suppose the Earth,of volume 1.08 × 10²¹ m³,was composed of water.How long would it take for the Earth at 0°C to reach 100°C,if none of the energy was radiated or reflected back out into space?

A)26.9 y
B)113 y
C)2.69 × 10⁴ y
D)1.13 × 10⁵ y
E)2.69 × 10⁷ y

Question 42

A 100 kg marble slab falls off a skyscraper and falls 200 m to the ground without hitting anyone.Its fall stops within milliseconds,so that there is no loss of thermal energy to its surroundings if its temperature is measured immediately after it stops.By how much has its temperature changed as a result of the fall,if we ignore energy gained or lost as a result of its interaction with the atmosphere? (
) )

A)0.57 °C
B)1.14 °C
C)2.28 °C
D)4.56 °C
E)22.8 °C

Question 43

A 100-g cube of ice is heated from −120°C to +120°C.In which of the following processes is the greatest amount of energy absorbed by this material?

A)warming ice to the melting point
B)melting the ice to become water
C)warming the resulting water
D)vaporizing the water to become steam
E)heating the steam

Question 44

A styrofoam container used as a picnic cooler contains a block of ice at 0°C.If 225 grams of ice melts in 1 hour,how much heat energy per second is passing through the walls of the container? (The heat of fusion of ice is 3.33 × 10⁵ J/kg).

Question 45

100 grams of liquid nitrogen at 77 K is stirred into a beaker containing 200 grams of 5°C water.If the nitrogen leaves the solution as soon as it turns to gas,how much water freezes? (The heat of evaporation of nitrogen is 6.09 cal/gram and the heat of fusion of water is 80 cal/gram. )

Question 46

In an isothermal process

A)P is constant.
B)V is constant.
C) is constant.
D)PV is constant.
E) is constant.

Question 47

We are able to define a mechanical equivalent for heat because

A)some thermal energy can be converted into mechanical energy.
B)mechanical energy can be converted into thermal energy.
C)work can be converted into thermal energy.
D)some thermal energy can be converted into work.
E)all of the above can occur.

Question 48

In braking an automobile,the friction between the brake drums and brake shoes converts the car's kinetic energy into heat.If a 1 500-kg automobile traveling at 30 m/s brakes to a halt,how much does the temperature rise in each of the four 8.0-kg brake drums? (The specific heat of each iron brake drum is 448 J/kg⋅°C).

Question 49

Which of the following substances has the greatest specific heat?

A)copper
B)ice
C)water
D)steam
E)Ice,water,and steam have equal specific heats since they are the same material,and this specific heat is greater than that of copper.

Question 50

Beryl states that insulation with the smallest possible thermal conductivity is best to keep a house warm in winter,but worst for keeping a house cool in summer.Sapphire insists the reverse is true: low thermal conductivity is good in the summer,but bad in the winter.Which one,if either is correct?

A)Beryl,because low thermal conductivity results in low heat transfer.
B)Beryl,because low thermal conductivity results in high heat transfer.
C)Sapphire,because low thermal conductivity results in low heat transfer.
D)Sapphire,because low thermal conductivity results in high heat transfer.
E)Neither,because low heat transfer is desirable both in summer and in winter.

Question 51

Which of the following statements is(are)correct when an ideal gas goes from an initial to a final state in a single process?

A)No work is done on or by the gas when the volume remains constant.
B)No energy is transferred into or out of the gas as heat transfer when the temperature remains constant.
C)The internal energy of the gas does not change when the pressure remains constant.
D)All the statements above are correct.
E)Only statements (a)and (b)above are correct.

Question 52

Duff states that equal masses of all substances have equal changes in internal energy when they have equal changes in temperature.Javan states that the change in internal energy is equal to a constant times the change in temperature for every ΔT,no matter how large or how small ΔT is,but that the constant is different for different substances.Which one,if either,is correct?

A)Neither,because the specific heat depends on the substance and may vary with temperature.
B)Neither,because a change of state may involve release or absorption of latent heat.
C)Neither because a substance may do work during a temperature change.
D)All of the statements above are correct.
E)Only statements (a)and (b)are correct.

Question 53

Steel blocks A and B,which have equal masses,are at T_A = 300 °C and T_B = 400 °C.Block C,with m_C = 2m_A,is at T_C = 350 °C.Blocks A and B are placed in contact,isolated,and allowed to come into equilibrium.Then they are placed in contact with block C.At that instant,

A)T_A = T_B < T_C.
B)T_A = T_B = T_C.
C)T_A = T_B > T_C.
D)T_A + T_B = T_C.
E)T_A − T_B = T_C.

Question 54

How much water at 20°C is needed to melt 1 kilogram of solid mercury at its melting point of −39°C? (The heat of fusion of mercury is 2.8 cal/gram).

Question 55

Aluminum rod #1 is 1.0 m long with cross-section area 2.0 cm².Aluminum rod #2 is 2.0 m long with cross-section area 4.0 cm².Aluminum rod #3 is 3.0 m long with cross-section area 9.0 cm².If each rod has the same temperature difference applied across its ends,which rod has the greatest rate of transfer of energy between its ends?

A)#1
B)#2
C)#3
D)#2 = #3,both greater than #1
E)They each have the same rate.

Question 56

A team of people who traveled to the North Pole by dogsled lived on butter because they needed to consume 6 000 dietician's Calories each day.Because the ice there is lumpy and irregular,they had to help the dogs by pushing and lifting the load.Assume they had a 16 hour working day and that each person could lift a 500 N load.How many times would a person have to lift this weight 1.00 m upwards in a constant gravitational field where
To do the work equivalent to 6 000 Calories?

A)50.2
B)492
C)5 130
D)50 200
E)492 000

Question 57

A block of material of mass m and specific heat c falls from height h and reaches speed v just before striking the ground.Its temperature is measured immediately after it strikes the ground.If we ignore any change in temperature owing to interaction with the air,the change in temperature of the block of material is

A) .
B) .
C) .
D)All of the answers above are correct.
E)Only (a)and (b)above are correct.

Question 58

In a thermodynamic process,the internal energy of a system in a container with adiabatic walls decreases by 800 J.Which statement is correct?

A)The system lost 800 J by heat transfer to its surroundings.
B)The system gained 800 J by heat transfer from its surroundings.
C)The system performed 800 J of work on its surroundings.
D)The surroundings performed 800 J of work on the system.
E)The 800 J of work done by the system was equal to the 800 J of heat transferred to the system from its surroundings.

Question 59

If a person in Alaska were locked out of his house on a day when the temperature outside was −40°C,his thick clothing would mostly reduce the loss of thermal energy by

A)conduction.
B)convection.
C)radiation.
D)all of the above.
E)convection and radiation.

Question 60

The R-value of an insulating material is the thickness of the material divided by its thermal conductivity.When an insulating material consists of three layers with R-values R₁,R₂ and R₃,the overall R-value of the insulation is given by

A)R = R₁ + R₂ + R₃.
B) .
C) .
D) .
E) .

Question 61

Star A has a radius of 200 000 km and a surface temperature of 6 000 K.Star B has a radius of 400 000 km and a surface temperature of 3 000 K.The emissivity of both stars is the same.What is the ratio of the rate of energy radiated by Star A to that of Star B?