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Heat and thermodynamics exercises · Physics Playground

ExercisesPhysics

Heat and thermodynamics

56 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Temperature & Heat, Gases & Pressure, Heat Flow & Equilibrium

Physics11.1 Temperature and Thermal Energy

ExampleConverting between Temperature Scales: Room TemperatureRoom temperature is generally defined to be 25 °C. (a) What is room temperature in °F? (b) What is it in K? Teacher Support Teacher Support In an alcohol-in-glass thermometer, alcohol molecules absorb energy by heat,…With a figure
ExampleConverting Between Temperature Scales: The Reaumur ScaleThe Reaumur scale is a temperature scale that was used widely in Europe in the 18th and 19th centuries. On the Reaumur temperature scale, the freezing point of water is 0 °R and the boiling temperature is 80 °R. If…

Physics11.2 Heat, Specific Heat, and Heat Transfer

ExampleCalculating the Required Heat: Heating Water in an Aluminum PanA 0.500 kg aluminum pan on a stove is used to heat 0.250 L of water from 20.0 °C to 80.0 °C. (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) the pan and (c) the water?
ExampleCalculating Temperature Increase: Truck Brakes Overheat on Downhill RunsWhen a truck headed downhill brakes, the brakes must do work to convert the gravitational potential energy of the truck to internal energy of the brakes. This conversion prevents the gravitational potential energy…With a figure

Physics11.3 Phase Change and Latent Heat

ExampleCalculating Heat Required for a Phase Change (part 1)Calculate a) how much energy is needed to melt 1.000 kg of ice at 0 °C (freezing point), and b) how much energy is required to vaporize 1.000 kg of water at 100 °C (boiling point).
ExampleCalculating Final Temperature from Phase Change: Cooling Soda with Ice CubesIce cubes are used to chill a soda at 20 °C and with a mass of msoda =0.25 kg. The ice is at 0 °C and the total mass of the ice cubes is 0.018 kg. Assume that the soda is kept in a foam container so that heat loss…

Physics12.2 First law of Thermodynamics: Thermal Energy and Work

ExampleCalculating Change in Internal EnergySuppose 40.00 J of energy is transferred by heat to a system, while the system does 10.00 J of work. Later, heat transfers 25.00 J out of the system, while 4.00 J is done by work on the system. What is the net change…
ExampleCalculating Change in Internal Energy: The Same Change in U is Produced by Two Different ProcessesWhat is the change in the internal energy of a system when a total of 150.00 J is transferred by heat from the system and 159.00 J is done by work on the system?

Physics12.3 Second Law of Thermodynamics: Entropy

ExampleEntropy Associated with DisorderFind the increase in entropy of 1.00 kg of ice that is originally at 0 °C and melts to form water at 0 °C.

Physics12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators

ExampleDaily Work Done by a Coal-Fired Power Station and Its Efficiency (part 1)A coal-fired power station is a huge heat engine. It uses heat to transfer energy from burning coal to do work to turn turbines, which are used then to generate electricity. In a single day, a large coal power…

College Physics13.1 Temperature

Example 13.1Converting between Temperature Scales: Room Temperature“Room temperature” is generally defined to be 25ºC. (a) What is room temperature in ºF? (b) What is it in K?
Quick checkDoes the temperature of a body depend on its size?

College Physics13.2 Thermal Expansion of Solids and Liquids

Example 13.3Calculating Linear Thermal Expansion: The Golden Gate BridgeThe main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from –15ºC to 40ºC. What is its change in length between these temperatures? Assume…
Example 13.4Calculating Thermal Expansion: Gas vs. Gas TankSuppose your 60.0-L (15.9-gal) steel gasoline tank is full of gas, so both the tank and the gasoline have a temperature of 15.0ºC. How much gasoline has spilled by the time they warm to 35.0ºC?
Example 13.5Calculating Thermal Stress: Gas PressureWhat pressure would be created in the gasoline tank considered in Example 13.4, if the gasoline increases in temperature from 15.0ºC to 35.0ºC without being allowed to expand? Assume that the bulk modulus B for…
Quick checkTwo blocks, A and B, are made of the same material. Block A has dimensions l×w×h=L×2L×L and Block B has dimensions 2L×2L×2L. If the temperature changes, what is (a) the change in the volume of the two blocks, (b) the…With a figure

College Physics13.3 The Ideal Gas Law

Example 13.6Calculating Pressure Changes Due to Temperature Changes: Tire PressureSuppose your bicycle tire is fully inflated, with an absolute pressure of 7.00×10^5 Pa (a gauge pressure of just under 90.0lb/in^2) at a temperature of 18.0ºC. What is the pressure after its temperature has risen to…
Example 13.7Calculating the Number of Molecules in a Cubic Meter of GasHow many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is. Calculate the number of molecules in a cubic meter…
Quick checkThe active ingredient in a Tylenol pill is 325 mg of acetaminophen (C8H9NO2). Find the number of active molecules of acetaminophen in a single pill.
Example 13.8Calculating Moles per Cubic Meter and Liters per MoleCalculate: (a) the number of moles in 1.00 m^3 of gas at STP, and (b) the number of liters of gas per mole.
Quick checkThe density of air at standard conditions (P=1atm and T=20ºC) is 1.28 kg/m^3. At what pressure is the density 0.64 kg/m^3 if the temperature and number of molecules are kept constant?
Example 13.9Calculating Number of Moles: Gas in a Bike TireHow many moles of gas are in a bike tire with a volume of 2.00×10^(–3)m^3(2.00 L), a pressure of 7.00×10^5Pa (a gauge pressure of just under 90.0lb/in^2), and at a temperature of 18.0ºC?
Quick checkLiquids and solids have densities about 1000 times greater than gases. Explain how this implies that the distances between atoms and molecules in gases are about 10 times greater than the size of their atoms and…

College Physics13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature

Example 13.10Calculating Kinetic Energy and Speed of a Gas Molecule(a) What is the average kinetic energy of a gas molecule at 20.0ºC (room temperature)? (b) Find the rms speed of a nitrogen molecule (N2) at this temperature.
Example 13.11Calculating Temperature: Escape Velocity of Helium AtomsIn order to escape Earth’s gravity, an object near the top of the atmosphere (at an altitude of 100 km) must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. At what temperature would…
Quick checkIf you consider a very small object such as a grain of pollen, in a gas, then the number of atoms and molecules striking its surface would also be relatively small. Would the grain of pollen experience any…

College Physics13.5 Phase Changes

Quick checkExplain why a cup of water (or soda) with ice cubes stays at 0ºC, even on a hot summer day.
Quick checkIs energy transfer involved in a phase change? If so, will energy have to be supplied to change phase from solid to liquid and liquid to gas? What about gas to liquid and liquid to solid? Why do they spray the orange…

College Physics13.6 Humidity, Evaporation, and Boiling

Example 13.12Calculating Density Using Vapor PressureTable 13.5 gives the vapor pressure of water at 20.0ºC as 2.33×10^3 Pa. Use the ideal gas law to calculate the density of water vapor in g/m^3 that would create a partial pressure equal to this vapor pressure.…
Example 13.13Calculating Humidity and Dew Point(a) Calculate the percent relative humidity on a day when the temperature is 25.0ºC and the air contains 9.40 g of water vapor per m^3. (b) At what temperature will this air reach 100% relative humidity (the…
Quick checkFreeze drying is a process in which substances, such as foods, are dried by placing them in a vacuum chamber and lowering the atmospheric pressure around them. How does the lowered atmospheric pressure speed the…

College Physics14.1 Heat

Quick checkTwo samples (A and B) of the same substance are kept in a lab. Someone adds 10 kilojoules (kJ) of heat to one sample, while 10 kJ of work is done on the other sample. How can you tell to which sample the heat was added?

College Physics14.2 Temperature Change and Heat Capacity

Example 14.1Calculating the Required Heat: Heating Water in an Aluminum PanA 0.500 kg aluminum pan on a stove is used to heat 0.250 liters of water from 20.0ºC to 80.0ºC. (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) the pan and (c) the…
Example 14.2Calculating the Temperature Increase from the Work Done on a Substance: Truck Brakes Overheat on Downhill RunsTruck brakes used to control speed on a downhill run do work, converting gravitational potential energy into increased internal energy (higher temperature) of the brake material. This conversion prevents the…
Example 14.3Calculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring Cold Water in a Hot PanSuppose you pour 0.250 kg of 20.0ºC water (about a cup) into a 0.500-kg aluminum pan off the stove with a temperature of 150ºC. Assume that the pan is placed on an insulated pad and that a negligible amount of water…
Quick checkIf 25 kJ is necessary to raise the temperature of a block from 25ºC to 30ºC, how much heat is necessary to heat the block from 45ºC to 50ºC?

College Physics14.3 Phase Change and Latent Heat

Example 14.4Calculate Final Temperature from Phase Change: Cooling Soda with Ice CubesThree ice cubes are used to chill a soda at 20ºC with mass msoda=0.25 kg. The ice is at 0ºC and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored.…
Quick checkWhy does snow remain on mountain slopes even when daytime temperatures are higher than the freezing temperature?

College Physics14.4 Heat Transfer Methods

Quick checkName an example from daily life (different from the text) for each mechanism of heat transfer.

College Physics14.5 Conduction

Example 14.5Calculating Heat Transfer Through Conduction: Conduction Rate Through an Ice BoxA Styrofoam ice box has a total area of 0.950 m^2 and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned beverages at 0ºC. The inside of the box is kept cold by melting ice. How much…
Example 14.6Calculating the Temperature Difference Maintained by a Heat Transfer: Conduction Through an Aluminum PanWater is boiling in an aluminum pan placed on an electrical element on a stovetop. The sauce pan has a bottom that is 0.800 cm thick and 14.0 cm in diameter. The boiling water is evaporating at the rate of 1.00 g/s.…
Quick checkHow does the rate of heat transfer by conduction change when all spatial dimensions are doubled?

College Physics14.6 Convection

Example 14.7Calculating Heat Transfer by Convection: Convection of Air Through the Walls of a HouseMost houses are not airtight: air goes in and out around doors and windows, through cracks and crevices, following wiring to switches and outlets, and so on. The air in a typical house is completely replaced in less…
Example 14.8Calculate the Flow of Mass during Convection: Sweat-Heat Transfer away from the BodyThe average person produces heat at the rate of about 120 W when at rest. At what rate must water evaporate from the body to get rid of all this energy? (This evaporation might occur when a person is sitting in the…
Quick checkExplain why using a fan in the summer feels refreshing!

College Physics14.7 Radiation

Example 14.9Calculate the Net Heat Transfer of a Person: Heat Transfer by RadiationWhat is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is 22.0ºC. The person has a normal skin temperature of 33.0ºC and a surface area of 1.50m^2.…
Quick checkWhat is the change in the rate of the radiated heat by a body at the temperature T1=20ºC compared to when the body is at the temperature T2=40ºC?

College Physics15.1 The First Law of Thermodynamics

Example 15.1Calculating Change in Internal Energy: The Same Change in U is Produced by Two Different Processes(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net…

College Physics15.2 The First Law of Thermodynamics and Some Simple Processes

Example 15.2Total Work Done in a Cyclical Process Equals the Area Inside the Closed Loop on a PV DiagramCalculate the total work done in the cyclical process ABCDA shown in Figure 15.12(b) by the following two methods to verify that work equals the area inside the closed loop on the PV diagram. (Take the data in the…

College Physics15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency

Example 15.3Daily Work Done by a Coal-Fired Power Station, Its Efficiency and Carbon Dioxide EmissionsA coal-fired power station is a huge heat engine. It uses heat transfer from burning coal to do work to turn turbines, which are used to generate electricity. In a single day, a large coal power station has…

College Physics15.4 Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated

Example 15.4Maximum Theoretical Efficiency for a Nuclear ReactorA nuclear power reactor has pressurized water at 300ºC. (Higher temperatures are theoretically possible but practically not, due to limitations with materials used in the reactor.) Heat transfer from this water is a…With a figure

College Physics15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators

Example 15.5The Best COP hp of a Heat Pump for Home UseA heat pump used to warm a home must employ a cycle that produces a working fluid at temperatures greater than typical indoor temperature so that heat transfer to the inside can take place. Similarly, it must produce…

College Physics15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

Example 15.6Entropy Increases in an Irreversible (Real) ProcessSpontaneous heat transfer from hot to cold is an irreversible process. Calculate the total change in entropy if 4000 J of heat transfer occurs from a hot reservoir at Th=600 K327º C to a cold reservoir at Tc=250…
Example 15.7Less Work is Produced by a Given Heat Transfer When Entropy Change is Greater(a) Calculate the work output of a Carnot engine operating between temperatures of 600 K and 100 K for 4000 J of heat transfer to the engine. (b) Now suppose that the 4000 J of heat transfer occurs first from the 600…
Example 15.8Entropy Associated with DisorderFind the increase in entropy of 1.00 kg of ice originally at 0º C that is melted to form water at 0º C.

College Physics15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

Example 15.9Entropy Increases in a Coin TossSuppose you toss 100 coins starting with 60 heads and 40 tails, and you get the most likely result, 50 heads and 50 tails. What is the change in entropy?