Thermal Equilibrium When you two systems are placed in contact with each other there is no net energy transfer between them. Consequently, these two systems would be at the same temperature. Zeroth Law of Thermodynamics If thermometer A is in thermal equilibrium with object B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. Therefore, the reading on A stays the same when A is moved over to make contact with C. Temperature What is temperature? Temperature is related to the thermal energy that is in a system. In a very practical sense, temperature is what we measure with a thermometer! In a glass-tube thermometer, such as the ones shown, a small volume of liquid expands or contracts when placed in contact with a hot or cold object. The object s temperature is determined by the length of the column of liquid. 2017 Pearson Education, Inc. Slide 19-3 1
Temperature The Celsius temperature scale is defined by setting T C = 0 for the freezing point of pure water, and T C = 100 for the boiling point. The Kelvin temperature scale has the same unit size as Celsius, with the zero point at absolute zero. The conversion from the Celsius scale to the Kelvin scale is T K = T C + 273.15 The Fahrenheit scale, still widely used in the United States, is defined by its relation to the Celsius scale, as follows: 2017 Pearson Education, Inc. Slide 19-4 Temperature 2017 Pearson Education, Inc. Slide 19-5 QuickCheck Which is the largest increase of temperature? A. An increase of 1ºF B. An increase of 1ºC C. An increase of 1 K D. Both B and C, which are the same and larger than A 2017 Pearson Education, Inc. Slide 19-6 2
Absolute Zero and Absolute Temperature Figure (a) shows a constantvolume gas thermometer. Figure (b) shows the pressuretemperature relationship for three different gases. There is a linear relationship between temperature and pressure. All gases extrapolate to zero pressure at the same temperature: T 0 = 273ºC This is called absolute zero, and forms the basis for the absolute temperature scale (Kelvin). 2017 Pearson Education, Inc. Slide 19-7 Example 1 - Temperature Conversion At what temperature does the numerical value in ºF match the numerical value in ºC? What is this temperature in Kelvin? Thermal Expansion Objects expand when heated. This thermal expansion is why the liquid rises in a thermometer and why pipes, highways, and bridges have expansion joints. The figure shows an object of length L that changes by ΔL when the temperature is changed from T to T + ΔT. For most solids, ΔL/L is proportional to ΔT with a proportionality coefficient α called the material s coefficient of linear expansion. 2017 Pearson Education, Inc. Slide 19-9 3
Coefficients of Linear and Volume Expansion 2017 Pearson Education, Inc. Slide 19-10 Example 2 Thermal Expansion A 55-m-long steel pipe runs from one side of a refinery to the other. By how much does the pipe s length increase on a 5ºC winter day when 155ºC oil is pumped through it? 2017 Pearson Education, Inc. Slide 19-11 Area and Volume Expansion Area and volume change during a temperature change ΔT, the fractional change in these quantities are A A = 2α T where β is the material s coefficient of volume expansion. Solids expand linearly in all three directions. The fractional change in volume is three times the fractional change in the length of the sides. Thus, β = 3α 2017 Pearson Education, Inc. Slide 19-12 4
QuickCheck A steel plate has a 2.000-cm-diameter hole through it. If the plate is heated, what happens to the diameter of the hole? A. It increases. B. It decreases. C. It stays the same. 2017 Pearson Education, Inc. Slide 19-13 Example 3 - Thermal Expansion Suppose a 60.0-L steel gasoline tank is full of gas that is cool because it has just been pumped from an underground reservoir. Now, 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? In-class Activity #1 A brass ring (α = 19 x 10-6 ºC -1 ) needs to fit over a steel rod (α = 12 x 10-6 ºC -1 ), but at 20 ºC the hole through the brass ring is 50 μm too small in diameter. The original diameter of both is close to 2.0 cm. To what temperature, in ºC, must the rod and ring be heated so that the ring just barely slips over the rod? 5
Heat In the 1840s James Joule showed that heat and work, previously regarded as completely different phenomena, are simply two different ways of transferring energy to or from a system. 2017 Pearson Education, Inc. Slide 19-16 Heat, Temperature, and Thermal Energy Thermal energy E th is an energy of the system due to the motion of its atoms and molecules. Heat Q is energy transferred between the system and the environment as they interact. Temperature T is a state variable that quantifies the hotness or coldness of a system. A temperature difference is required in order for heat to be transferred between the system and the environment. 2017 Pearson Education, Inc. Slide 19-17 The Sign of Heat 2017 Pearson Education, Inc. Slide 19-18 6
Units of Heat The SI unit of heat is the Joule. Historically, a unit for measuring heat, the calorie, had been defined as 1 calorie = 1 cal = the quantity of heat needed to change the temperature of 1 g of water by 1ºC In today s SI units, the conversion is 1 cal = 4.186 J The calorie you know in relation to food is not the same as the heat calorie: 1 food calorie = 1 Cal = 1000 cal = 1 kcal = 4186 J 2017 Pearson Education, Inc. Slide 19-19 Temperature Change and Specific Heat The amount of energy that raises the temperature of 1 kg of a substance by 1 K is called the specific heat c of that substance. If W = 0, so no work is done by or on the system, then the heat needed to bring about a temperature change ΔT is The molar specific heat C is the amount of energy that raises the temperature of 1 mol of a substance by 1 K. 2017 Pearson Education, Inc. Slide 19-20 QuickCheck Two liquids, A and B, have equal masses and equal initial temperatures. Each is heated for the same length of time over identical burners. Afterward, liquid A is hotter than liquid B. Which has the larger specific heat? A. Liquid A B. Liquid B C. There s not enough information to tell. 2017 Pearson Education, Inc. Slide 19-21 7
Specific Heats of Various Materials 2017 Pearson Education, Inc. Slide 19-22 Example 4 Specific Heat A 70 kg student catches the flu, and his body temperature increases from 37.0C to 39.0C. How much energy is required to raise his body s temperature? The specific heat of a human body is roughly 3500 J/kg K. 2017 Pearson Education, Inc. Slide 19-23 QuickCheck 1 kg of silver (c = 234 J/kg K) is heated to 100ºC. It is then dropped into 1 kg of water (c = 4190 J/kg K) at 0ºC in an insulated beaker. After a short while, the common temperature of the water and silver is A. 0ºC B. Between 0ºC and 50ºC C. 50ºC D. Between 50ºC and 100ºC 2017 Pearson Education, Inc. Slide 19-24 8
Example 5 - Specific Heat Problem A 0.500-kg aluminum pan on a stove and 0.250 L of water in it are heated 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 water? In-class Activity #2 Suppose you pour 0.250 kg of 20.0ºC water into a 0.500-kg aluminum pan at a temperature of 150ºC. What is the temperature when the water and pan reach thermal equilibrium? Assume no heat transfer, boiling nor evaporation takes place. 9