Question 1

Suppose working outside on a hot day someone generate 450 J of heat each second.If this energy is compensated for by the evaporation of sweat,how much water would be lost in an hour? The latent heat of fusion for water is 334 kJ/kg and for vaporization is 2,200 kJ/kg.

Accepted Answer

First, we need to find out how much energy is produced in an hour:
450 J/s x 60 s/min x 60 min/hr = 1,620,000 J/hr

We know that all of this energy is being used to evaporate sweat. The amount of water that needs to be evaporated can be calculated using the formula:

ΔHv = m x Lv

where:
ΔHv = heat of vaporization = 2,200 kJ/kg
Lv = latent heat of vaporization for water
m = mass of water

Solving for m:

m = ΔHv / Lv

m = 2,200,000 J / 2,200,000 J/kg

m = 1 kg

This means that for every kg of water that evaporates, 2,200,000 J of energy is absorbed. So, to absorb 1,620,000 J of energy, the mass of water that needs to evaporate can be calculated as:

1,620,000 J / 2,200,000 J/kg = 0.74 kg or 0.74 L

Therefore, the amount of water lost in an hour is 0.74 L, which is answer choice B.

Question 2

In the text there is a table of coefficients of linear (α)and volume (β)expansions due to temperature changes.For the solid materials in this list,there is a relationship between α and β which allows you to find the value of β if you know α.Which of the following best describes that relationship?

Accepted Answer

The relationship between the linear expansion coefficient (α) and the volume expansion coefficient (β) for solid materials is given by β = 3α. This is because volume expansion is roughly three times the linear expansion in each dimension (length, width, height) for isotropic materials.

Question 3

A metal bar is used to conduct heat.When the temperature at one end is 100°C and at the other is 20°C,heat is transferred at a rate of 32 J/s.The bar is then stretched uniformly to twice its original length.If again it has ends at 100°C and 20°C,at what rate will heat be transferred between it ends?

Accepted Answer

When the bar is stretched to twice its length, its cross-sectional area is halved, reducing the rate of heat transfer by a factor of 4 (since rate is proportional to area and inversely proportional to length). Thus, the new rate is 32 J/s divided by 4, which is 8 J/s.

Question 4

At 20°C an aluminum ring has an inner diameter of 5.000 cm,and a brass rod has a diameter of 5.020 cm.Keeping the brass rod at 20°C,which of the following temperatures of the ring will allow the ring to just slip over the brass rod? (α_Al = 2.4 × 10−⁵ /°C,α_brass = 1.9 × 10−⁵/°C )

Accepted Answer

The answer of At 20°C an aluminum ring has an...

Question 5

A silver bar of length 30 cm and cross-sectional area 2.0 cm² is used to transfer heat from a 100°C reservoir to a 0°C block of ice.How much ice is melted per second? (For silver,k = 427 W / m · °C.For ice,L_f = 334,000 J/kg. )

Accepted Answer

The answer of A silver bar of length 30 cm...

Question 6

A metal bar is used to conduct heat.When the temperature at one end is 100°C and at the other is 20°C,heat is transferred at a rate of 16 J/s.If the temperature of the hotter end is reduced to 60°C,what will be the rate of heat transfer?

Accepted Answer

The rate of heat transfer in a metal bar is directly proportional to the temperature difference. Using the formula Q/t = k*A*(Thot-Tcold)/L, where Q/t is the rate of heat transfer, k is the thermal conductivity of the metal, A is the cross-sectional area of the bar, L is the length of the bar, and Thot and Tcold are the temperatures of the hot and cold ends, respectively. Since all other factors are constant, we can set up a proportion: (Thot1 - Tcold)/(Thot2 - Tcold) = Q1/Q2. Substituting the given values, we get (100-20)/(60-20) = 16/Q2, solving for Q2, we get Q2 = 8 J/s. Therefore, the rate of heat transfer when the temperature of the hotter end is reduced to 60°C is 8 J/s.

Question 7

Carly places one end of a steel bar in a Bunsen flame and the other end in an ice cube.By what factor is the rate of heat flow changed when the bar's cross-sectional area is tripled?

Accepted Answer

The rate of heat flow is directly proportional to the cross-sectional area of the bar. Therefore, if the cross-sectional area is tripled, the rate of heat flow will also be tripled. So, the factor by which the rate of heat flow changes is 3.0. Hence, the answer is (C).

Question 8

Dmitri places one end of a copper rod in a heat reservoir and the other end in a heat sink.By what factor is the rate of heat flow changed when the temperature difference between the reservoir and sink is doubled?

Accepted Answer

The answer of Dmitri places one end of a copper...

Question 9

The inside of a house is at 20°C on an early morning when the temperature outside is 15°C.The next morning the inside temperature is the same,but the outside temperature is now 5°C.How much does the energy per unit time lost by conduction through the walls,windows,doors,etc. ,change for the house from the first morning to the second one.

Accepted Answer

The energy loss by conduction is proportional to the temperature difference between inside and outside. On the first morning, the difference is 5°C, and on the second morning, it is 15°C. Therefore, the energy loss triples.

Question 10

A pipe of length 10.0 m increases in length by 2.0 cm when its temperature is increased by 90°F.What is its coefficient of linear expansion?

Accepted Answer

The answer of A pipe of length 10.0 m increases...

Question 11

Suppose the ends of a 20-m long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 15 cm².What force does the beam exert when it is heated to 40°C? (α_steel = 1.1 × 10−⁵/C°,Y_steel = 2.0 × 10¹¹ N/m²)

Accepted Answer

The force exerted by the beam can be calculated using the formula F = Y * A * α * ΔT, where Y is Young's modulus, A is the cross-sectional area, α is the coefficient of linear expansion, and ΔT is the change in temperature. Substituting the given values, F = (2.0 × 10^11 N/m²) * (15 × 10^-4 m²) * (1.1 × 10^-5 /°C) * (40°C) = 1.32 × 10^5 N, which is approximately 1.3 × 10^5 N.

Question 12

I place a 250-g ice cube (initially at 0°C)in a Styrofoam box with wall thickness 1.0 cm and total surface area 600 cm².If the air surrounding the box is at 20°C and after 2 hours the ice is completely melted,what is the conductivity of the Styrofoam material? (L_f = 80 cal/g)

Accepted Answer

The answer of I place a 250-g ice cube (initially...

Question 13

A long steel beam has a length of fifty meters on a cold day when the temperature is 0°C.What is the length of the beam on a hot day when T = 40°C? (α_steel= 1.1 × 10−⁵/°C)

Accepted Answer

The answer of A long steel beam has a length...

Question 14

A steel piano string is attached,under tension,at each end to secure posts.When gently struck,a faint note can be detected coming from the string.The string is then cooled by blowing cold air over it and then is struck again.How does the note now detected compare to the previous one.

Accepted Answer

Cooling the steel piano string causes it to contract, increasing the tension in the string. This increased tension results in a higher frequency of vibration when the string is struck, producing a note of higher pitch.

Question 15

A windowpane is half a centimeter thick and has an area of 2.0 m².The temperature difference between the inside and outside surfaces of the pane is 15°C.What is the rate of heat flow through this window? (Thermal conductivity for this glass is 0.84 W / m ·°C. )

Accepted Answer

The rate of heat flow through a windowpane is given by the equation:Q = k * A * (T1 - T2) / dwhere:Q is the rate of heat flow in wattsk is the thermal conductivity of the glass in W / m ·°CA is the area of the windowpane in m2T1 is the temperature of the inside surface of the windowpane in °CT2 is the temperature of the outside surface of the windowpane in °Cd is the thickness of the windowpane in mIn this problem, we are given the following information:k = 0.84 W / m ·°CA = 2.0 m2T1 = 15°CT2 = 0°Cd = 0.005 mPlugging these values into the equation, we get:Q = 0.84 W / m ·°C * 2.0 m2 * (15°C - 0°C) / 0.005 mQ = 5040 WTherefore, the rate of heat flow through the windowpane is 5040 W, which is closest to choice A, 5000 J/s.

Question 16

An automobile gas tank is filled to its capacity of 20.00 gallons with the gasoline at an initial temperature of 10°C.The automobile is parked in the Sun causing the gasoline's temperature to rise to 60°C.If the coefficient of volume expansion for gasoline is 9.6 × 10−⁴/°C,what volume runs out the overflow tube? Assume the change in volume of the tank is negligible.

Accepted Answer

First, we need to find the expansion of gasoline due to the change in temperature. Using the formula for volume expansion, we have:

ΔV = VαΔT

where ΔV is the change in volume, V is the initial volume (20.00 gallons), α is the coefficient of volume expansion for gasoline (9.6 × 10^-4 /°C), and ΔT is the change in temperature (60°C - 10°C = 50°C).

Plugging in the values, we get:

ΔV = (20.00 gal) x (9.6 × 10^-4 /°C) x (50°C) = 0.96 gal

This means that the gasoline expands by 0.96 gallons as it heats up. Since the tank is already full, the excess gasoline will flow out the overflow tube. Therefore, the volume that runs out the overflow tube is 0.96 gallons.

The best choice is B, 0.96 gallon.

Question 17

As a copper wire is heated,its length increases by 0.200%.What is the change of the temperature of the wire? (α_Cu = 16.6 × 10−⁶/C°)

Accepted Answer

The change in length is given by:ΔL = αLΔTwhere α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.Solving for ΔT, we get:ΔT = ΔL/(αL)Substituting the given values, we get:ΔT = (0.00200)/(16.6 × 10−6 × L)Since the length is not given, we cannot calculate the exact value of ΔT. However, we can say that the change in temperature is proportional to the change in length. Therefore, the correct answer is A) 120°C, which is the largest change in temperature given.

Question 18

A steel sphere sits on top of an aluminum ring.The steel sphere (α = 1.10 × 10−⁵/°C)has a diameter of 4.0000 cm at 0°C.The aluminum ring (α = 2.40 × 10−⁵/°C)has an inside diameter of 3.9900 cm at 0°C.Closest to which temperature given will the sphere just fall through the ring?

Accepted Answer

The sphere will fall through the ring when their diameters are equal. Using the formula for linear expansion, the temperature at which the sphere's diameter equals the ring's diameter can be calculated. Solving for the temperature gives approximately 193°C.

Question 19

A 2.00-kg copper rod is 40.00 cm long at 23°C.If 50,000 J are transferred to the rod by heat,what is its change in length? (c_copper = 387 J/kg·°C and α_copper = 17 × 10^-6/°C)

Accepted Answer

First, we need to calculate the change in temperature of the copper rod using the formula:
ΔT = Q/mcΔT
where Q is the heat energy transferred, m is the mass of the rod, c is the specific heat capacity of copper, and ΔT is the change in temperature.
ΔT = (50000 J) / (2 kg * 387 J/kg·°C) = 64.59°C
Next, we can calculate the change in length using the formula:
ΔL = αLΔT
where α is the coefficient of linear expansion for copper and L is the original length of the rod.
ΔL = (17 × 10^-6/°C) * (40 cm) * (64.59°C) = 0.0439 cm
Rounding to three significant figures yields an answer of 0.044 cm, which is choice B.

Question 20

Two stars,A and B,have the same emissivity,but the radii and surface temperatures are different with R_A = 2 R_B,and T_A = 0.5 T_B.Assuming the temperature of space to be negligible,which star radiates the most energy per unit time?

Accepted Answer

The rate at which energy radiated from a star is given by the Stefan-Boltzmann law, which states that the energy radiated per unit time per unit surface area is proportional to the fourth power of the surface temperature. Since both stars have the same emissivity, the one with the larger surface area (star B) will radiate more energy per unit time. Additionally, since the surface temperature of star B is higher than that of star A, the energy radiated per unit area will be even greater. Therefore, star B radiates more energy per unit time.

Quiz 14: Sound: Part A

Suppose working outside on a hot day someone generate 450 J of heat each second.If this energy is compensated for by the evaporation of sweat,how much water would be lost in an hour? The latent heat of fusion for water is 334 kJ/kg and for vaporization is 2,200 kJ/kg.

At 20°C an aluminum ring has an inner diameter of 5.000 cm,and a brass rod has a diameter of 5.020 cm.Keeping the brass rod at 20°C,which of the following temperatures of the ring will allow the ring to just slip over the brass rod? (α_Al = 2.4 × 10−⁵ /°C,α_brass = 1.9 × 10−⁵/°C )

A silver bar of length 30 cm and cross-sectional area 2.0 cm² is used to transfer heat from a 100°C reservoir to a 0°C block of ice.How much ice is melted per second? (For silver,k = 427 W / m · °C.For ice,L_f = 334,000 J/kg. )

A metal bar is used to conduct heat.When the temperature at one end is 100°C and at the other is 20°C,heat is transferred at a rate of 16 J/s.If the temperature of the hotter end is reduced to 60°C,what will be the rate of heat transfer?

Carly places one end of a steel bar in a Bunsen flame and the other end in an ice cube.By what factor is the rate of heat flow changed when the bar's cross-sectional area is tripled?

Dmitri places one end of a copper rod in a heat reservoir and the other end in a heat sink.By what factor is the rate of heat flow changed when the temperature difference between the reservoir and sink is doubled?

A pipe of length 10.0 m increases in length by 2.0 cm when its temperature is increased by 90°F.What is its coefficient of linear expansion?

Suppose the ends of a 20-m long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 15 cm².What force does the beam exert when it is heated to 40°C? (α_steel = 1.1 × 10−⁵/C°,Y_steel = 2.0 × 10¹¹ N/m²)

I place a 250-g ice cube (initially at 0°C) in a Styrofoam box with wall thickness 1.0 cm and total surface area 600 cm².If the air surrounding the box is at 20°C and after 2 hours the ice is completely melted,what is the conductivity of the Styrofoam material? (L_f = 80 cal/g)

A long steel beam has a length of fifty meters on a cold day when the temperature is 0°C.What is the length of the beam on a hot day when T = 40°C? (α_steel= 1.1 × 10−⁵/°C)

A steel piano string is attached,under tension,at each end to secure posts.When gently struck,a faint note can be detected coming from the string.The string is then cooled by blowing cold air over it and then is struck again.How does the note now detected compare to the previous one.

A windowpane is half a centimeter thick and has an area of 2.0 m².The temperature difference between the inside and outside surfaces of the pane is 15°C.What is the rate of heat flow through this window? (Thermal conductivity for this glass is 0.84 W / m ·°C. )

As a copper wire is heated,its length increases by 0.200%.What is the change of the temperature of the wire? (α_Cu = 16.6 × 10−⁶/C°)

A steel sphere sits on top of an aluminum ring.The steel sphere (α = 1.10 × 10−⁵/°C) has a diameter of 4.0000 cm at 0°C.The aluminum ring (α = 2.40 × 10−⁵/°C) has an inside diameter of 3.9900 cm at 0°C.Closest to which temperature given will the sphere just fall through the ring?

A 2.00-kg copper rod is 40.00 cm long at 23°C.If 50,000 J are transferred to the rod by heat,what is its change in length? (c_copper = 387 J/kg·°C and α_copper = 17 × 10^-6/°C)

Two stars,A and B,have the same emissivity,but the radii and surface temperatures are different with R_A = 2 R_B,and T_A = 0.5 T_B.Assuming the temperature of space to be negligible,which star radiates the most energy per unit time?

Quiz 14: Sound: Part A

Suppose working outside on a hot day someone generate 450 J of heat each second.If this energy is compensated for by the evaporation of sweat,how much water would be lost in an hour? The latent heat of fusion for water is 334 kJ/kg and for vaporization is 2,200 kJ/kg.

At 20°C an aluminum ring has an inner diameter of 5.000 cm,and a brass rod has a diameter of 5.020 cm.Keeping the brass rod at 20°C,which of the following temperatures of the ring will allow the ring to just slip over the brass rod? (αAl = 2.4 × 10−5 /°C,αbrass = 1.9 × 10−5/°C )

A silver bar of length 30 cm and cross-sectional area 2.0 cm2 is used to transfer heat from a 100°C reservoir to a 0°C block of ice.How much ice is melted per second? (For silver,k = 427 W / m · °C.For ice,Lf = 334,000 J/kg. )

A metal bar is used to conduct heat.When the temperature at one end is 100°C and at the other is 20°C,heat is transferred at a rate of 16 J/s.If the temperature of the hotter end is reduced to 60°C,what will be the rate of heat transfer?

Carly places one end of a steel bar in a Bunsen flame and the other end in an ice cube.By what factor is the rate of heat flow changed when the bar's cross-sectional area is tripled?

Dmitri places one end of a copper rod in a heat reservoir and the other end in a heat sink.By what factor is the rate of heat flow changed when the temperature difference between the reservoir and sink is doubled?

A pipe of length 10.0 m increases in length by 2.0 cm when its temperature is increased by 90°F.What is its coefficient of linear expansion?

Suppose the ends of a 20-m long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 15 cm2.What force does the beam exert when it is heated to 40°C? (αsteel = 1.1 × 10−5/C°,Ysteel = 2.0 × 1011 N/m2)

I place a 250-g ice cube (initially at 0°C) in a Styrofoam box with wall thickness 1.0 cm and total surface area 600 cm2.If the air surrounding the box is at 20°C and after 2 hours the ice is completely melted,what is the conductivity of the Styrofoam material? (Lf = 80 cal/g)

A long steel beam has a length of fifty meters on a cold day when the temperature is 0°C.What is the length of the beam on a hot day when T = 40°C? (αsteel= 1.1 × 10−5/°C)

A steel piano string is attached,under tension,at each end to secure posts.When gently struck,a faint note can be detected coming from the string.The string is then cooled by blowing cold air over it and then is struck again.How does the note now detected compare to the previous one.

A windowpane is half a centimeter thick and has an area of 2.0 m2.The temperature difference between the inside and outside surfaces of the pane is 15°C.What is the rate of heat flow through this window? (Thermal conductivity for this glass is 0.84 W / m ·°C. )

As a copper wire is heated,its length increases by 0.200%.What is the change of the temperature of the wire? (αCu = 16.6 × 10−6/C°)

A steel sphere sits on top of an aluminum ring.The steel sphere (α = 1.10 × 10−5/°C) has a diameter of 4.0000 cm at 0°C.The aluminum ring (α = 2.40 × 10−5/°C) has an inside diameter of 3.9900 cm at 0°C.Closest to which temperature given will the sphere just fall through the ring?

A 2.00-kg copper rod is 40.00 cm long at 23°C.If 50,000 J are transferred to the rod by heat,what is its change in length? (ccopper = 387 J/kg·°C and αcopper = 17 × 10-6/°C)

Two stars,A and B,have the same emissivity,but the radii and surface temperatures are different with RA = 2 RB,and TA = 0.5 TB.Assuming the temperature of space to be negligible,which star radiates the most energy per unit time?

At 20°C an aluminum ring has an inner diameter of 5.000 cm,and a brass rod has a diameter of 5.020 cm.Keeping the brass rod at 20°C,which of the following temperatures of the ring will allow the ring to just slip over the brass rod? (α_Al = 2.4 × 10−⁵ /°C,α_brass = 1.9 × 10−⁵/°C )

A silver bar of length 30 cm and cross-sectional area 2.0 cm² is used to transfer heat from a 100°C reservoir to a 0°C block of ice.How much ice is melted per second? (For silver,k = 427 W / m · °C.For ice,L_f = 334,000 J/kg. )

Suppose the ends of a 20-m long steel beam are rigidly clamped at 0°C to prevent expansion.The rail has a cross-sectional area of 15 cm².What force does the beam exert when it is heated to 40°C? (α_steel = 1.1 × 10−⁵/C°,Y_steel = 2.0 × 10¹¹ N/m²)

I place a 250-g ice cube (initially at 0°C) in a Styrofoam box with wall thickness 1.0 cm and total surface area 600 cm².If the air surrounding the box is at 20°C and after 2 hours the ice is completely melted,what is the conductivity of the Styrofoam material? (L_f = 80 cal/g)

A long steel beam has a length of fifty meters on a cold day when the temperature is 0°C.What is the length of the beam on a hot day when T = 40°C? (α_steel= 1.1 × 10−⁵/°C)

A windowpane is half a centimeter thick and has an area of 2.0 m².The temperature difference between the inside and outside surfaces of the pane is 15°C.What is the rate of heat flow through this window? (Thermal conductivity for this glass is 0.84 W / m ·°C. )

As a copper wire is heated,its length increases by 0.200%.What is the change of the temperature of the wire? (α_Cu = 16.6 × 10−⁶/C°)

A steel sphere sits on top of an aluminum ring.The steel sphere (α = 1.10 × 10−⁵/°C) has a diameter of 4.0000 cm at 0°C.The aluminum ring (α = 2.40 × 10−⁵/°C) has an inside diameter of 3.9900 cm at 0°C.Closest to which temperature given will the sphere just fall through the ring?

A 2.00-kg copper rod is 40.00 cm long at 23°C.If 50,000 J are transferred to the rod by heat,what is its change in length? (c_copper = 387 J/kg·°C and α_copper = 17 × 10^-6/°C)

Two stars,A and B,have the same emissivity,but the radii and surface temperatures are different with R_A = 2 R_B,and T_A = 0.5 T_B.Assuming the temperature of space to be negligible,which star radiates the most energy per unit time?