Thermo-physics practice
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1. Work it out
Original textbook practice · AP Physics 2 topic
A 5.0 kg carbon block initially at 500°C receives 10 MJ. In the supplied simplified material model, c_solid = 0.71 J/(g·K), the listed melting threshold is 3550°C, c_liquid = 0.850 J/(g·K), c_gas = 0.843 J/(g·K), the listed boiling threshold is 4057°C, L_f = 8.74 kJ/g and L_v = 59.5 kJ/g. Calculate its final temperature within this model and determine whether the listed phase thresholds are reached.
Original problem 1
This is a constant-specific-heat exercise using the provided table. Real carbon’s high-temperature phase behavior depends on pressure and allotrope; its listed melting/boiling data are not a general atmospheric-pressure phase diagram. The unused phase data do not affect this calculation.
Problem text
A 5.0 kg carbon block initially at 500°C receives 10 MJ. In the supplied simplified material model, c_solid = 0.71 J/(g·K), the listed melting threshold is 3550°C, c_liquid = 0.850 J/(g·K), c_gas = 0.843 J/(g·K), the listed boiling threshold is 4057°C, L_f = 8.74 kJ/g and L_v = 59.5 kJ/g. Calculate its final temperature within this model and determine whether the listed phase thresholds are reached.
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2. Work it out
Original textbook practice · AP Physics 2 topic
The source states that a 100 kg metal block at 80°C is placed in 200 mL of water initially at 15°C and the final temperature is 65°C. Take water density as 1.00 g/mL and c_w = 4.18 J/(g·K), ignore the container and heat loss, and infer the metal’s specific heat. Comment on the plausibility of the source mass and resulting value.
Original problem 2
The source mass is preserved. Changing it to 100 g would yield 27.9 J/(g·K), which is also not a justified ordinary-metal value.
Problem text
The source states that a 100 kg metal block at 80°C is placed in 200 mL of water initially at 15°C and the final temperature is 65°C. Take water density as 1.00 g/mL and c_w = 4.18 J/(g·K), ignore the container and heat loss, and infer the metal’s specific heat. Comment on the plausibility of the source mass and resulting value.
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3. Work it out
Original textbook practice · AP Physics 2 topic
An insulated calorimeter contains 500 mL of water at 20°C. Add 5.0 g of iron with c = 0.45 J/(g·K) and 20 g of aluminum with c = 0.91 J/(g·K), both at 80°C. Use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Neglect the calorimeter’s heat capacity. Find the final equilibrium temperature.
Original problem 3
Problem text
An insulated calorimeter contains 500 mL of water at 20°C. Add 5.0 g of iron with c = 0.45 J/(g·K) and 20 g of aluminum with c = 0.91 J/(g·K), both at 80°C. Use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Neglect the calorimeter’s heat capacity. Find the final equilibrium temperature.
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4. Work it out
Original textbook practice · AP Physics 2 topic
A copper bar of mass 2.0 kg and initial length 0.50 m absorbs 175 kJ. Take c = 0.39 J/(g·K) and the source-table linear expansion coefficient α = 17 × 10⁻⁶ K⁻¹ as constant. Assume the bar remains solid and expands freely. Find its final length.
Original problem 4
The source-table copper coefficient is supplied explicitly. An initial temperature is unnecessary for the length change with constant c and α, but remaining below a phase transition is required.
Problem text
A copper bar of mass 2.0 kg and initial length 0.50 m absorbs 175 kJ. Take c = 0.39 J/(g·K) and the source-table linear expansion coefficient α = 17 × 10⁻⁶ K⁻¹ as constant. Assume the bar remains solid and expands freely. Find its final length.
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5. Work it out
Original textbook practice · AP Physics 2 topic
A 200 mL sample of water begins at 80°C. A cooling device removes energy at a constant rate of 10 J/s. Use water density 1.00 g/mL, c_w = 4.18 J/(g·K), L_f = 334 J/g and a freezing temperature of 0°C at approximately atmospheric pressure. Ignore the cup and heat leaks. Find the time to turn all the water into ice at 0°C.
Original problem 5
Problem text
A 200 mL sample of water begins at 80°C. A cooling device removes energy at a constant rate of 10 J/s. Use water density 1.00 g/mL, c_w = 4.18 J/(g·K), L_f = 334 J/g and a freezing temperature of 0°C at approximately atmospheric pressure. Ignore the cup and heat leaks. Find the time to turn all the water into ice at 0°C.
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6. Work it out
Original textbook practice · AP Physics 2 topic
The source silver-block diagram has a heated face 50 m high by 20 m wide and a heat-flow length of 45 m. With conductivity k = 428 W/(m·K), keep one face at 300°C and the opposite face at 25°C. Assume one-dimensional steady conduction, insulated side faces and constant k. How much energy passes through the block during 10 s?
Original problem 6
The original wording that heat “takes 10 s until reaching the other side” is not a steady-conduction boundary condition. A transient heating calculation would additionally need the initial temperature profile, density and specific heat. The dimensions are retained as meters, as shown.
Problem text
The source silver-block diagram has a heated face 50 m high by 20 m wide and a heat-flow length of 45 m. With conductivity k = 428 W/(m·K), keep one face at 300°C and the opposite face at 25°C. Assume one-dimensional steady conduction, insulated side faces and constant k. How much energy passes through the block during 10 s?
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7. Work it out
Original textbook practice · AP Physics 2 topic
A steel cube initially has volume 1.00 cm³ at 150°C and density 7.85 g/cm³ at that temperature. Its specific heat is 0.49 J/(g·K). Place it into 500 mL of water at 65°C in an ideal insulated calorimeter; use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Take steel’s source-table α = 11 × 10⁻⁶ K⁻¹ as constant. Find the final temperature, edge length and volume, neglecting the container.
Original problem 7
The source’s 1 cm³ means an initial volume, and the source-table steel coefficient is 11 × 10⁻⁶ K⁻¹. Density is used once to find mass at the initial state, not reapplied as a temperature-independent constraint on final volume.
Problem text
A steel cube initially has volume 1.00 cm³ at 150°C and density 7.85 g/cm³ at that temperature. Its specific heat is 0.49 J/(g·K). Place it into 500 mL of water at 65°C in an ideal insulated calorimeter; use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Take steel’s source-table α = 11 × 10⁻⁶ K⁻¹ as constant. Find the final temperature, edge length and volume, neglecting the container.
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8. Work it out
Original textbook practice · AP Physics 2 topic
Compare the energy required to bring 6.0 kg of water from 90°C and 9.0 kg of acetone from 20°C to gases at 400°C. Use the source’s idealized constant-property model at approximately atmospheric pressure: water boils at 100°C, c_liquid = 4.18 J/(g·K), c_gas = 1.86 J/(g·K), L_v = 2230 J/g; acetone boils at 56°C, c_liquid = 2.18 J/(g·K), c_gas = 1.28 J/(g·K), L_v = 549 J/g. Neglect losses and chemical reactions.
Original problem 8
The source table interchanges the two fusion values, but fusion is not used in this exercise. The 400°C gas calculations are simplified constant-property estimates; acetone chemical stability and temperature-dependent heat capacities are outside the model.
Problem text
Compare the energy required to bring 6.0 kg of water from 90°C and 9.0 kg of acetone from 20°C to gases at 400°C. Use the source’s idealized constant-property model at approximately atmospheric pressure: water boils at 100°C, c_liquid = 4.18 J/(g·K), c_gas = 1.86 J/(g·K), L_v = 2230 J/g; acetone boils at 56°C, c_liquid = 2.18 J/(g·K), c_gas = 1.28 J/(g·K), L_v = 549 J/g. Neglect losses and chemical reactions.
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9. Work it out
Original textbook practice · AP Physics 2 topic
An ideal calorimeter contains 500 mL of water at 20°C. A 5.0 g iron sample with c_Fe = 0.45 J/(g·K), heated separately to 80°C, is placed in the water and allowed to equilibrate. Remove the iron without removing any water, reheat it to 80°C, return it, and allow a second equilibration. Use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Find the second equilibrium temperature, neglecting the container and losses.
Original problem 9
Problem text
An ideal calorimeter contains 500 mL of water at 20°C. A 5.0 g iron sample with c_Fe = 0.45 J/(g·K), heated separately to 80°C, is placed in the water and allowed to equilibrate. Remove the iron without removing any water, reheat it to 80°C, return it, and allow a second equilibration. Use water density 1.00 g/mL and c_w = 4.18 J/(g·K). Find the second equilibrium temperature, neglecting the container and losses.
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10. Work it out
Original textbook practice · AP Physics 2 topic
A steel antenna has length 20.0 m at 20°C. Use the source-table α = 11 × 10⁻⁶ K⁻¹ as constant. Find its lengths at −5°C and 50°C and the length increase as the day warms between these temperatures.
Original problem 10
Problem text
A steel antenna has length 20.0 m at 20°C. Use the source-table α = 11 × 10⁻⁶ K⁻¹ as constant. Find its lengths at −5°C and 50°C and the length increase as the day warms between these temperatures.
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Additional practice
11. Where Celsius and Fahrenheit agree
Original textbook practice · AP Physics 2 topic
Find the temperature for which the Celsius and Fahrenheit readings are equal. Then convert a temperature rise of 30°F into a rise in kelvins.
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12. Mix two water samples
Original textbook practice · AP Physics 2 topic
Mix 250 g of water at 80°C with 400 g of water at 15°C in an insulated container of negligible heat capacity. Find the final temperature, assuming no phase change.
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13. Include the calorimeter itself
Original textbook practice · AP Physics 2 topic
Place 0.20 kg of brass at 100°C into 0.25 kg of water initially at 20°C in a calorimeter also initially at 20°C. The calorimeter heat capacity is 150 J/K. Use c_brass = 380 J/(kg·K) and c_water = 4180 J/(kg·K). The combined system is insulated. Find its final temperature.
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14. Efficient electric kettle
Original textbook practice · AP Physics 2 topic
A 1000 W kettle transfers 80% of its electrical energy into 0.50 kg of water. Find the time to heat the water from 18°C to 95°C, using c_w = 4180 J/(kg·K). Neglect the kettle’s heat capacity and evaporation.
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15. Brake heating from a stop
Original textbook practice · AP Physics 2 topic
A bicycle and rider of total mass 75 kg stop from 12 m/s. Half of their initial translational kinetic energy is absorbed by a 1.0 kg steel brake assembly. Use c_steel = 490 J/(kg·K). Find the assembly’s temperature rise, ignoring wheel spin and cooling during the stop.
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16. Partial melting after warming ice
Original textbook practice · AP Physics 2 topic
A 0.100 kg ice sample starts at −20°C and receives 20.0 kJ at atmospheric pressure. Use c_ice = 2100 J/(kg·K) and L_f = 334,000 J/kg. Find its final temperature and the masses of liquid water and remaining ice.
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17. Ice cools a drink
Original textbook practice · AP Physics 2 topic
Add 50 g of ice at −10°C to 200 g of water at 40°C in an ideal insulated cup. Use c_ice = 2.10 J/(g·K), c_water = 4.18 J/(g·K), and L_f = 334 J/g. Find the final temperature and determine whether all the ice melts.
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18. Steam condenses into water
Original textbook practice · AP Physics 2 topic
Inject 10.0 g of steam at 100°C into 200 g of water at 20°C in an insulated vessel at atmospheric pressure. All steam condenses and no water escapes. Use L_v = 2257 J/g and c_water = 4.18 J/(g·K). Find the final temperature and verify that it is below 100°C.
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19. Read material properties from a heating curve
Original textbook practice · AP Physics 2 topic
A heater delivers a constant 50 W to a 0.040 kg pure sample with negligible heat losses. A single-phase segment rises by 20 K in 40 s, then a phase-change plateau lasts 120 s at constant pressure. Find the specific heat on the rising segment and the latent heat of the transition.
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20. Wax cools and solidifies
Original textbook practice · AP Physics 2 topic
A 30 g pure wax sample starts liquid at 80°C and ends solid at 20°C. Its melting point is 60°C, liquid specific heat is 2.4 J/(g·K), solid specific heat is 2.0 J/(g·K), and latent heat of fusion is 200 J/g. Find the magnitude and sign of heat transferred to the wax.
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21. Length of a heated brass wire
Original textbook practice · AP Physics 2 topic
A brass wire is 0.750 m long at 20°C and is freely heated to 100°C. With constant α = 19 × 10⁻⁶ K⁻¹, find its extension and final length.
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22. A hole in a heated plate
Original textbook practice · AP Physics 2 topic
An aluminum plate has a circular hole of diameter 20.0 mm at 20°C. Heat the unconstrained plate uniformly to 170°C. With α = 23 × 10⁻⁶ K⁻¹, find the hole’s new diameter. Explain whether the hole grows or shrinks.
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23. Differential expansion of two rails
Original textbook practice · AP Physics 2 topic
An aluminum rail and a steel rail each have length 2.00 m at 10°C, with their left ends aligned. They are free to expand when heated to 80°C. Use α_aluminum = 23 × 10⁻⁶ K⁻¹ and α_steel = 11 × 10⁻⁶ K⁻¹. By how much do their right ends separate?
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24. Density changes when a liquid expands
Original textbook practice · AP Physics 2 topic
Ethanol has density 789 kg/m³ at 20°C. A fixed mass is warmed to 50°C. In the linear volume-expansion model use β = 1.10 × 10⁻³ K⁻¹ and neglect evaporation. Find its final density.
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25. Thermal stress in a constrained steel rod
Original textbook practice · AP Physics 2 topic
A steel rod is fixed firmly at both ends so its length cannot change. It warms by 40 K. Use Young’s modulus E = 200 GPa and α = 11 × 10⁻⁶ K⁻¹. In the elastic small-strain model, determine the stress needed to cancel its free thermal expansion and state whether it is tensile or compressive.
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26. Heat conducted through window glass
Original textbook practice · AP Physics 2 topic
A glass pane has area 2.0 m² and thickness 6.0 mm. Maintain its faces at 22°C and 2°C. With k = 1.0 W/(m·K), find the steady conduction rate and the energy transmitted in 30 min. Ignore surface-film resistance and edge losses.
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27. Composite wall and interface temperature
Original textbook practice · AP Physics 2 topic
A wall of area 8.0 m² has 0.12 m of brick (k = 0.60 W/(m·K)) next to 0.040 m of foam (k = 0.030 W/(m·K)). The brick-side outer face is held at 20°C and the foam-side outer face at −10°C. Find the steady heat rate and the brick–foam interface temperature, neglecting contact and surface resistances.
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28. Radiative cooling at the initial instant
Original textbook practice · AP Physics 2 topic
A small body with mass 0.20 kg, specific heat 900 J/(kg·K), radiating area 0.10 m² and emissivity 0.80 is initially at 400 K in a large 300 K enclosure. Find its initial net radiative heat-loss rate and initial cooling rate. Ignore convection and conduction. Use σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴).
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29. Convective heat transfer from a panel
Original textbook practice · AP Physics 2 topic
A panel’s surface is maintained at 50°C in moving air at 25°C. Its exposed area is 1.5 m². For this flow the convective heat-transfer coefficient is h = 8.0 W/(m²·K), with P_out = hA(T_surface − T_air). Find the heat-loss rate and the energy lost in 5.0 min.
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30. Calorimetry with a measured heat leak
Original textbook practice · AP Physics 2 topic
Mix a 0.50 kg copper object at 90°C with 0.30 kg water at 20°C. During equilibration the combined system loses 5.00 kJ to the room. Use c_copper = 390 J/(kg·K), c_water = 4180 J/(kg·K), and negligible container heat capacity. Find the final common temperature.
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