physics
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PROBLEM SET
PHY12 – January 21, 2015
Thermal Physics
1. The coefficient of volumetric expansion for gold is 4.20 × 10 –5/C°. The density of gold is 19
300 kg/m3 at 0.0 °C. What is the density of gold at 1050 °C?
2. A copper wire and a lead wire are joined together, end to end. The compound wire has an
effective coefficient of linear expansion of 20 x 10 -6 / C. What fraction of the length of the
compound wire is copper?
coefficient of linear expansion of copper is 17 x 10-6/C
coefficient of linear expansion of lead is 29 x 10-6/C
3. A concrete walk is poured on a day when the temperature is 20°C in such a way that the ends
are unable to move.
(a) What is the stress in the cement on a hot day of 50°C?
(b) Does the concrete fracture?
Young's modulus for concrete to be 7109 N/m2; compressive strength to be 2 109 N/m2
Coefficient of linear expansion of concrete is 12x10-6/C.
4. Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of
mercury and ethyl alcohol. If the expansion of the glass is taken into account, how many
times greater is the distance between the degree marks on the ethyl alcohol thermometer
than that on the mercury thermometer?
mercury = 1.82 x 10-4/C ; ethyl alcohol = 1.12 x 10-4/C; glass, pyrex = 3.2 x 10-6/C
5. A 100-g sample of ice at 0.0 °C falls through a distance of 50 m and undergoes a completely
inelastic collision with the earth. If all of the mechanical energy is absorbed by the ice, how
much of it melts?
6. A woman finds the front window of her house covered with ice at -12oC. The ice has a
thickness of 5x10-4 m and the window has an area of 1.3 m2. The density of the ice is 917
kg/m3. How much heat is required to melt the ice? Specific heat of ice = 2100 J/kg C o.
7. The brass bar and aluminum bar in the drawing are
attached to an immovable wall. At 28°C the air
gap between the rods is 2.5x10-3 m. At what
temperature will the gap be closed?
ALUMINUM = 23 x 10-6/C ; BRASS = 19 x 10-6/C
8. You are very particular about the temperature of beverages. You want to cool 2 liters of hot
tea (essentially water) from a temperature of 98C to 1C by adding ice from a freezer at 20C. How much ice should be added to accomplish the task? Neglect any heat transfer to
the environment.
9. A cylindrical copper rod of length 1.2 m and cross-sectional area 4.8 cm2 is insulated to
prevent thermal energy from being transferred through its surface. The ends are maintained
at a temperature difference of 100C by having one end in a water-ice mixture and the other
in boiling water and steam.
(a) Find the rate at which thermal energy is conducted along the rod.
(b) Find the rate at which ice melts at the cold end.
10. Three building materials, plasterboard (k=0.30 J/(s-m-C°), brick
(k=0.60 J/(s-m-C°), and wood (k=0.10J/(s-m-C°), are
sandwiched together as the drawing illustrates.
The
temperatures at the inside and outside surfaces are 27°C and
0°C, respectively. Each material has the same thickness and
cross-sectional area. Find the temperature (a) at the plasterboard-brick interface and (b) at the brick-wood interface.
11. Ethyl alcohol has a boiling point of 78C, a freezing point of -114C, a heat of vaporization of
879 kJ/kg, a heat of fusion of 109 kJ/kg, and a specific heat of 2.34 kJ/kg-C. How much
thermal energy must be added to 0.510 kg of ethyl alcohol that is initially solid at -114C, so
that it becomes a gas at 78C?
ADDITIONAL PROBLEMS
1. On a linear X temperature scale, water freezes at -125°X and boils at 375°X. On a linear
temperature Y scale, water freezes at -70°Y and boils at -30°Y. A temperature of 75 °Y
corresponds to what temperature on the X scale?
2. A container made of aluminum [ = 72 x10-6 (C°)-1] has a volume of 1.50x10-3 m3. Into this
container is placed 1.10x10-3 m3 of glycerol [ = 5x10-4 (C°)-1]. Both the aluminum and the
glycerol have the same temperature. By what amount T should the temperature of the
container and the glycerol within it be increased, so that the liquid just begins to spill out?
3. A Styrofoam box used to keep drinks cold at a picnic has a total wall area (including the lid) of
1.75 m2 and a wall thickness of 8 cm. It is filled with ice, water, and cans of cola at 0°C. a)
What is the rate of heat flow into the box if the temperature of the outside wall is 38°C? b)
How much ice melts in four hours? (Thermal Conductivity of Styrofoam = 0.010 W/m∙ K)
4. 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? (Latent heat of fusion is 80 cal/g;
Latent
heat of condensation is -540 cal/g; specific heat of water is 1 cal/g-C°)
5. Three rectangular metal bars of
identical cross-section area (0.5 m2)
are welded end to end as shown. The
free end of the aluminum bar is
immersed in steam to keep its
temperature at 100oC. The free end of the copper bar is soaked in ice bath to maintain its
temperature at 0oC. Thermal conductivities (W/m-C°): Aluminum = 205, Brass = 109 and
Copper = 385.
a. What is the temperature at the interface of the aluminum and brass bars?
b. What is the temperature at the interface of the brass and copper bars?
PHY12 – January 21, 2015
Thermal Physics
1. The coefficient of volumetric expansion for gold is 4.20 × 10 –5/C°. The density of gold is 19
300 kg/m3 at 0.0 °C. What is the density of gold at 1050 °C?
2. A copper wire and a lead wire are joined together, end to end. The compound wire has an
effective coefficient of linear expansion of 20 x 10 -6 / C. What fraction of the length of the
compound wire is copper?
coefficient of linear expansion of copper is 17 x 10-6/C
coefficient of linear expansion of lead is 29 x 10-6/C
3. A concrete walk is poured on a day when the temperature is 20°C in such a way that the ends
are unable to move.
(a) What is the stress in the cement on a hot day of 50°C?
(b) Does the concrete fracture?
Young's modulus for concrete to be 7109 N/m2; compressive strength to be 2 109 N/m2
Coefficient of linear expansion of concrete is 12x10-6/C.
4. Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of
mercury and ethyl alcohol. If the expansion of the glass is taken into account, how many
times greater is the distance between the degree marks on the ethyl alcohol thermometer
than that on the mercury thermometer?
mercury = 1.82 x 10-4/C ; ethyl alcohol = 1.12 x 10-4/C; glass, pyrex = 3.2 x 10-6/C
5. A 100-g sample of ice at 0.0 °C falls through a distance of 50 m and undergoes a completely
inelastic collision with the earth. If all of the mechanical energy is absorbed by the ice, how
much of it melts?
6. A woman finds the front window of her house covered with ice at -12oC. The ice has a
thickness of 5x10-4 m and the window has an area of 1.3 m2. The density of the ice is 917
kg/m3. How much heat is required to melt the ice? Specific heat of ice = 2100 J/kg C o.
7. The brass bar and aluminum bar in the drawing are
attached to an immovable wall. At 28°C the air
gap between the rods is 2.5x10-3 m. At what
temperature will the gap be closed?
ALUMINUM = 23 x 10-6/C ; BRASS = 19 x 10-6/C
8. You are very particular about the temperature of beverages. You want to cool 2 liters of hot
tea (essentially water) from a temperature of 98C to 1C by adding ice from a freezer at 20C. How much ice should be added to accomplish the task? Neglect any heat transfer to
the environment.
9. A cylindrical copper rod of length 1.2 m and cross-sectional area 4.8 cm2 is insulated to
prevent thermal energy from being transferred through its surface. The ends are maintained
at a temperature difference of 100C by having one end in a water-ice mixture and the other
in boiling water and steam.
(a) Find the rate at which thermal energy is conducted along the rod.
(b) Find the rate at which ice melts at the cold end.
10. Three building materials, plasterboard (k=0.30 J/(s-m-C°), brick
(k=0.60 J/(s-m-C°), and wood (k=0.10J/(s-m-C°), are
sandwiched together as the drawing illustrates.
The
temperatures at the inside and outside surfaces are 27°C and
0°C, respectively. Each material has the same thickness and
cross-sectional area. Find the temperature (a) at the plasterboard-brick interface and (b) at the brick-wood interface.
11. Ethyl alcohol has a boiling point of 78C, a freezing point of -114C, a heat of vaporization of
879 kJ/kg, a heat of fusion of 109 kJ/kg, and a specific heat of 2.34 kJ/kg-C. How much
thermal energy must be added to 0.510 kg of ethyl alcohol that is initially solid at -114C, so
that it becomes a gas at 78C?
ADDITIONAL PROBLEMS
1. On a linear X temperature scale, water freezes at -125°X and boils at 375°X. On a linear
temperature Y scale, water freezes at -70°Y and boils at -30°Y. A temperature of 75 °Y
corresponds to what temperature on the X scale?
2. A container made of aluminum [ = 72 x10-6 (C°)-1] has a volume of 1.50x10-3 m3. Into this
container is placed 1.10x10-3 m3 of glycerol [ = 5x10-4 (C°)-1]. Both the aluminum and the
glycerol have the same temperature. By what amount T should the temperature of the
container and the glycerol within it be increased, so that the liquid just begins to spill out?
3. A Styrofoam box used to keep drinks cold at a picnic has a total wall area (including the lid) of
1.75 m2 and a wall thickness of 8 cm. It is filled with ice, water, and cans of cola at 0°C. a)
What is the rate of heat flow into the box if the temperature of the outside wall is 38°C? b)
How much ice melts in four hours? (Thermal Conductivity of Styrofoam = 0.010 W/m∙ K)
4. 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? (Latent heat of fusion is 80 cal/g;
Latent
heat of condensation is -540 cal/g; specific heat of water is 1 cal/g-C°)
5. Three rectangular metal bars of
identical cross-section area (0.5 m2)
are welded end to end as shown. The
free end of the aluminum bar is
immersed in steam to keep its
temperature at 100oC. The free end of the copper bar is soaked in ice bath to maintain its
temperature at 0oC. Thermal conductivities (W/m-C°): Aluminum = 205, Brass = 109 and
Copper = 385.
a. What is the temperature at the interface of the aluminum and brass bars?
b. What is the temperature at the interface of the brass and copper bars?
