H. SAIBI December 10 th, 2014

A pilot, a hot air balloonist, and a scuba diver must all have a good working understanding of air and water temperatures as they flights and dives.

 What is temperature?  What is it a measurement of?  Our sense of touch can usually tell us if an object is hot or cold.  If an object is heated or cooled, some of its physical properties change.  If a solid or liquid is heated, its volume increases.  If a gas is heated and its pressure is kept constant, its pressure increases.  If an electrical conductor is heated, its electrical resistance changes.  A physical property that changes with temperature is called a thermometric property.  Contact between a warm copper bar and a cold iron bar, so the copper bar cools and the iron bar warms, we say that the two bars are in Thermal contact. The copper bar contracts slightly as it cools, and the iron bar expands slightly as it warms.  This process eventually stops and the lengths remain constant. The two bars are then in thermal equilibrium with each other.

 If two objects are in thermal equilibrium with a third object, then all three of the objects are in thermal equilibrium with each other.  Two objects are defined to have the same temperature if they are in thermal equilibrium with each other. The Zeroth law enables us to define a temperature scale.

©2008 by W.H. Freeman and Company Fig. The Zeroth law of thermodynamics. (a) Systems A and B are in thermal contact with system C, but not with each other. When A and B are each in thermal equilibrium with C, they are in thermal equilibrium with each other, which can be checked by placing them in contact with each other as in Part (b).

 Thermometers are devices used to measure the temperature of a system. All thermometers are based on the principle that some physical property of a system changes at the system’s temperature changes. Some physical properties that change with temperature are:  The volume of a liquid  The dimensions of a solid  The pressure of a gas at constant volume  The volume of a gas at constant pressure  The electric resistance of a conductor  The color of an object.

 Type of thermometers: mercury or alcohol. Mercury is highly toxic. Today alcohol is commonly used in thermometers.  The mercury thermometer consists of a glass bulb and tube containing a fixed amount of mercury. When this thermometer is put in contact with a warmer object, the mercury expands, increasing the length of the mercury column.  We can create a scale along the glass tube by using the following procedure:  First the thermometer is placed in ice and water in equilibrium at a pressure of 1 atm. When the thermometer is in thermal equilibrium with the ice water gives the ice-point temperature (normal freezing point of water).  Next, the thermometer is placed in boiling water at a pressure of 1 atm. When the thermometer is in thermal equilibrium with the boiling water gives the steam-point temperature (normal boiling point of water).

 This scales defines the ice-point temperature as zero degrees centigrade and the steam- point temperature as 100 degrees centigrade. Length of mercury column The centigrade temperature: Length of mercury column when the thermometer is in an ice bath Length of mercury column when the thermometer is in a steam bath. Normal temperature of the human body is about 37 o C.

 German physicist: Daniel Fahrenheit.  Widely used in the United States defines the ice-point temperature as 32 o F and the steam-point temperature as 212 o F.  There are 100 centigrade degrees and 180 Fahrenheit degrees between the ice and steam points.  A temperature change of one centigrade degree therefore equals a change of 9/5 (1.8) Fahrenheit degrees. Fahrenheit-Centigrade Conversion:

 Other thermometric properties can be used to set up thermometers and construct temperature scales. ©2008 by W.H. Freeman and Company Fig. A bimetallic strip. When heated or cooled, the two metals expand or contract by different amounts, causing the strip to bend.

©2008 by W.H. Freeman and Company Fig. (a) A thermometer using a bimetallic strip in the form of coil (the red pointer is attached to one end of the coil). When the temperature of the coil increases, the needle rotates clockwise because the outer metal expands more than the inner metal. (b) A home thermostat controls the central air conditioner. When the air gets warmer, the coil expands, the glass bulb mounted on it tills, and mercury in the tube slides to close an electrical switch, turning on the air conditioning. A slide lever (at the lower right), used to rotate the coil mount, is used to set the desired temperature. The circuit will be broken when the cooler air causes the bimetallic coil to contract.

 The different types of centigrade thermometers (calibrated in ice water and steam) give slightly different readings at points between 0 o C and 100 o C.  Discrepancies increase above the steam point and below the ice point.  However, in one group of thermometers, gas thermometers, measured temperatures agree closely with each other, even far from the calibration points.  In a constant-volume gas thermometer, the gas volume is kept constant, and change in gas pressure is used to indicate a change in temperature.

©2008 by W.H. Freeman and Company Fig. A constant-volume gas thermometer. The volume is kept constant by raising or lowering tube B 3 so that the mercury in tube B 2 remains at the zero mark. The temperature is chosen to be proportional to the pressure of the gas in tube B 1, which is indicated by height h of the mercury column in tube B 3.

 An ice-point pressure P o and steam-point pressure P 100 are determined by placing the thermometer in ice-water and water-steam baths, and the interval between them is divided into 100 equal degrees (for the centigrade scale).  If the pressure is P t in a bath whose temperature is to be determined, that temperature in degrees centigrade is defined to be: Constant-Volume Centigrade Gas Thermometer

©2008 by W.H. Freeman and Company Fig. Temperature of the boiling point of sulfur measured with constant-volume gas thermometers filled with various gases. Increasing or decreasing the amount of gas in the thermometer varies the pressure P 100 at the steam point of water. As the amount of gas is reduced, the temperature of the boiling point of sulfur measured by all the thermometers approaches the value o C. Note that the temperature axis shows a range of temperatures from 444 o C to 446 o C.

©2008 by W.H. Freeman and Company Fig. Plot of pressure versus temperature for a gas, as measured by a constant-volume gas thermometer. When extrapolated to zero pressure, the plot intersects the temperature axis at the value o C.

 A reference state that is much more precisely reproducible than either ice or steam points is the triple point of water – the unique temperature and pressure at which water, water vapor, and ice coexist in equilibrium. This equilibrium occurs at 4.58 mmHg and 0.01 o C. The ideal-gas temperature scale is defined so that the temperature of the triple-point state is K (Kelvins). ©2008 by W.H. Freeman and Company Fig. Water at its triple point. The spherical flask contains liquid water, ice, and water vapor in thermal equilibrium.

Constant-Volume ideal- gas-temperature thermometer  The temperature T of any state is defined to be proportional to the pressure in a constant-volume gas thermometer:  Where P is the observed pressure of the gas in the thermometer, P 3 is the pressure when the thermometer is immersed in a water-ice-vapor bath at its triple point, and T 3 =273.16K (the triple-point temperature). The value P 3 depends on the amount of gas in the thermometer. T is absolute temp.  Zero on the Celsius scale corresponds to an ideal-gas temperature of exactly K.  The lowest temperature that can be measured with a constant-volume gas thermometer is about 20 K, and requires helium for the gas. Below this temperature helium liquefies; all other gases liquefy at higher temperatures (see next Table).

©2008 by W.H. Freeman and Company Celsius-Absolute Conversion  To convert from degrees Celsius to Kelvins, we merely add :