Chapter 14 – Temperature and Heat
Introduction
Contents:
- Temperature and thermal equilibrium
- Thermometer and temperature scale
- Heat conduction
- Heat convection and radiation
- Thermal Expansion
Objectives
1. Explain the concept of temperature and heat
2. Define and explain thermal equilibrium and the Zeroth Law of Thermodynamics
3. Explain physical changes of thermometric quantities such as change of volume, length, gas pressure, electrical resistance and radiated wavelength of hot body.
4. State the absolute temperature and the values of pressure and temperature for the triple point of water.
5. Write and use the relationship between temperature and thermometric quantities for ideal gas temperature scale T= 273.16K and the celcius temperature scale T = 100 0C.
6. Explain mechanism of heat transfer through solids and distinguish the conduction of heat through metal and non-metal solids.
7. Define thermal conductivity and application of the equation for one dimensional heat transfer.
8. Investigate quantitatively heat conduction through combination of rods of different materials, insulated and non-insulated rods, good and bad conductor.
9. explain the mechanism of natural and forced heat convection.
10. Explain the mechanism of heat transfer through radiation and use the equation of the Stefan-Boltzmann law
11. Define and use the principle of linear, area and volume thermal expansion and state the relationship between them.
12. Understand thermal expansion of water at 4 0C
Conceptual Map of Chapter 14
INTRODUCTION
As we discuss thermal properties of a body or system, we always relate it to temperature, a fundamental physical quantity. How does the hot air differ from cold air? We use thermometers to record the temperature. We also like to relate the temperature and heat. In this chapter we would like to examine the nature of heat and the ways in which we measure temperature.
14.1 – Temperature and thermal equilibrium
Temperature is defined as a relative measure of hotness or coldness. Scientifically, it is a scalar quantity that is same for the two systems in thermal equilibrium.
When a hot body is in thermal contact with a cold body, gradually both bodies will experience the same temperature. Both objects are in thermal equilibrium as two or more systems having same temperature. It is based on the Zeroth Law of Thermodynamics which states that if object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object C is also in thermal equilibrium with object A.
14.2 Thermometer and temperature scale
Temperature scale is used to determine the temperature of a body quantitatively. There are three types of temperature scale – Celsius, Fahrenheit and Kelvin with unit of 0C, 0F and K respectively. Fortunately, many physical properties of materials change sufficiently with temperature to be used as the bases for thermometers. The ice point and the steam point of water are two convenient fixed points are the temperatures at which pure water freezes and boils under the pressure of 1 atm (standard pressure). The boiling and freezing points is defined as equilibrium temperature for water and steam at standard pressure.
On the Celsius scale, ice point is labeled as 0 0C and steam point as 1000C, whereas on the Fahrenheit scale, both are labeled at 32 0F and 212 0F respectively. On the Celsius scale, there are 100 equal intervals; on the Fahrenheit scale, there are 180 intervals. Therefore, Celsius degree is larger than a Fahrenheit degree.
Kelvin scale is introduced after it is found that the minimum temperature under this temperature, the concept of temperature is meaningless. This temperature is designated as the absolute zero. On the Kelvin scale, it is written as 0K, ice point as 273.15 K and steam point as 373.15K. Kelvin scale is also called as absolute temperature scale or ideal gas law temperature scale.
The relationship of these temperature scales can be written as:
TC is for Celsius; TF is for Fahrenheit and TK is for Kelvin.
Sample question:
If the room temperature is measured at 270C, what is temperature on the kelvin and Fahrenheit scale?
Solution:
TK = TC +273.15
= 27 +273.15
» 300K
TF = TC +320
= 270 +320
= 80.6 0F
Note: For distinction, a particular temperature measurement, such as 200C, is written with 0C whereas a temperature interval, such as DT = 800C – 600C = 20 C0 (pronounced 20 Celsius degrees).
14.3 Thermometer
Thermometer is an instrument to measure temperature. The operation principle is based on physical properties that change with temperature. These properties are called thermometric quantities. Commonly, thermometric quantities can change linearly with temperature and be measurable.
For instance, the thermometer that is commonly used is mercury thermometer. The thermal expansion of mercury is a thermometric property and the volume is used as thermometric quantity. Due to the fixed crossed sectional area, thermometer can have the length of the capillary of mercury as thermometric quantity.
The following chart shows the type of thermometer with its thermometric quantity.
Type / Thermometric quantityMercury in capillary tube / length (l)
constant volume gas / pressure (p)
Constant pressure gas / volume (v)
Thermocouple / electro motive force (emf)
Electrical resistance / resistance (ohm)
Pyrometer / colour
A good thermometer should have following properties:
· Accuracy – big change of material thermometric quantity with respect to the small change of temperature.
· Precision –a precise reading can be taken with respect to the real temperature
· Reliability – the same temperature can be recorded after repetitive measurement.
· Sensitivity – thermal equilibrium can be achieved with the system and temperature can be measured instantly.
Besides, a practical thermometer should be portable, continuously readable, fixed phase of material that is used within the wide range of measurement and the working material should change realistically and linearly with respect to temperature.
14.4 Relationship of temperature and thermometric quantities.
Let X be the thermometric quantity, which is p, V, R, Î or l. If thermometer with quantity X is measured at ice and steam points, Xi and Xs, the temperature T at Celsius scale can be written as:
which X is the value of thermometric quantity at temperature T. Therefore, temperature T can be written in Fahrenheit scale as:
General equation for any temperature scale is as follows:
Problem:
The length of mercury for mercury thermometer is used to measure the temperature of unknown liquid is 0.5 cm at 0 0C and 13.0 cm at 100 0C. Determine the temperature of the liquid if the length of mercury is 6.0 cm.
Solution:
Option 1
If the length of mercury capillary tube is linearly changed with temperature T, the general equation is:
T = k l + c
with k and c are constant. At the lower scale (0 0C) and upper scale (100 0C), the equations become:
Ti = k li + c
Ts = k ls + c
If both equations is solved simultaneously, therefore,
k = = 8.0 0C/cm
c = Ti – k i = Ti - k s = - 4.0 0C
Therefore
T = (8.0 0C/cm) - 4.0 0C
For =6.0 cm,
T = (8.0 0C/cm)(6.0) - 4.0 0C = 44.0 0C
Option 11
Use the general equation
14.5 The constant-volume gas thermometer
Thermometric quantity for X is pressure, p of a gas with fixed mass and constant volume. A simple type of the thermometer is shown below.
A constant-volume gas thermometer measures the pressure of the gas contained in the flask immersed in the bath. The volume of gas in the flask is kept constant by raising or lowering reservoir B such that the mercury level in column A remains constant.
The bulb contains the gas is immersed in the bath with higher temperature. The gas temperature increases, the gas expands and raises mercury level in tube B. The pressure of the gas in the bulb can be written as:
p = p0 + rgh
p0 is atmospheric pressure, r is mercury density, g is gravity and h is height difference of mercury level.
If the bulb is place in the environment at different temperature T, the pressure p is also changed. The change of p against T from various gases is shown in the following chart.
Note that, for all gases, the pressure extrapolates to zero at the unique temperature of –273.15 0C.
The linear relationship between pressure p and temperature T can be written generally as:
T = kp
with k as a constant.
The fixed point for the measurement is the triple point of water where the steam, water and ice exist in equilibrium. The triple point for water is at 0.01 0C or 273.16K. Therefore the equation can be written as:
pt is the pressure at the triple point of water. Thus the relation of T and p can be written as,
T = p
If the bulb containing certain type of gas (oxygen, hydrogen, nitrogen or air) is place in the boiling water, the graph of T against p is shown as follows.
From the above graph, even different type of gas is used, the same reading of temperature at steam point is recorded with the condition that the pressure is negligible. The graph also confirms that when the pressure is lowered, the real gases properties disappear and act like ideal gas. The details of ideal gas property will be explained in gas kinetic theory.
The measured temperature at zero pressure does not depend on type and the amount of gas is used. Thus, the temperature at ideal gas scale can be defined as,
14.8 Latent heat and phase change
The material commonly exists in phase of solid, liquid or vapor. In the solid phase, the molecules have strong bond that they cannot move freely and only vibrate at equilibrium. The molecules in liquid move freely but still have strong bond that they could not escape easily from the liquid surface. The gas molecules move more freely than the liquid.
As the material experiences the phase change, for instance from solid to liquid or from liquid to gas, the temperature remain constant even heat is added to the molecules. While the molecules has the phase change, the heat never increases the mean kinetic energy of molecules, but it is used to overcome the bond among the molecules. The heat involved in the phase change of molecules is known as latent heat. Thus, the amount of heat Q affects the mass of m of the material can be written as,
Q = m L
The latent heat for a solid-liquid phase change is called the latent heat of fusion (Lf) and that for a liquid-gas phase change is called the latent heat of vaporization (Lv). These often referred to as simply the heat of fusion and the heat of vaporization.
During melting and vaporization, heat is needed by water. On the other hand, the heat is released from water during freezing and condensation.
The pressure should remain constant during the phase change. It can effect the boiling and ice point. For instance, if the pressure is above 1 atm, the water will boil above 100 0C and more heat is needed to increase the temperature.
Problem:
How much heat is required for 50 g ice at 0 0C to vaporize completely to be steam at 1000C?
Solution:
There are three stages to be considered.
- The phase change, melting of ice at 0 0C
- The temperature increase from 0 0C to 1000C
- The phase change, vaporization of water at 100 0C
Thus, the amount of heat is required,
Q = m Lf + mc DT + m Lv
= 0.05( 333 + 4200(100) +2264)
=21, 130 kJ.
14. 9 Heat (thermal energy transfer)
Conduction of heat occurs when the temperature of a body is not uniform. For instance, a rod is heat at one end of the rod. The heat flows from the hot end to the cold end. In the microscopic level, the heat transfer can be described as the transfer of kinetic energy of molecules of high kinetic energy to the low kinetic energy molecules. In the gas phase, the transfer of heat is through the collision of molecules. In solid phase, the molecules only vibrate at equilibrium point. The molecules has more vibration at hot region, thus has more kinetic energy. The kinetic energy is transferred to the adjacent molecules which result the transfer of heat through solid.
Most metals are good conductors whereas non-metals are weak heat conductors or good heat insulators. The reason is metals have more free electrons that act as the agents of heat transfer. On the other hand, non-metals have few free electrons. Gases are good heat insulators because the distance between atoms or molecules is extremely large.
Let us consider heat conduction through a rod which has cross sectional area A and length x as shown below.
Let say the cold end has temperature of T1 and the hot end has temperature of T2. The heat flows from T2 to T1. The transfer rate of heat through the rod is proportional to the cross-sectional area and the temperature difference, DT and inversely proportional to the length of the rod. We can deduce the rate of heat conduction as,
or
where k is known as thermal conductivity coefficient. is called temperature gradient. The negative sign show the heat is transferred downward the temperature gradient.
The ability of the material to conduct heat depends on thermal conductivity, k. The bigger k, the better the ability of matter to conduct heat. Material with small k value becomes a good insulator.