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PX121: Thermal Physics Lecture 2 http://www2.warwick.ac.uk/fac/sci/physics/ teach/module_home/px121/ [email protected] Room P447 Department of Physics Introduction VII Equilibrium - Le Chatelier’s Principle “A system in equilibrium reacts to a (small) externally imposed change in one of its state variables by readjusting its internal condition so as to reverse the change.” (Henri Louis le Chatelier, 1844) E.g. If there is a small heat flow into a gas in equilibrium with its surroundings, its temperature will increase. However, the temperature will now be higher than that of the surroundings, so heat will flow out of the gas, and its temperature will decrease again. Thermal equilibrium Definition: two systems are in thermal equilibrium if their state variables (p, V, T) do not change when they are put in contact via a diathermal wall. Department of Physics S1 S2 Introduction VIII Leads to “Zeroeth Law of Thermodynamics: “If systems S1 and S2 are separately in thermal equilibrium with system S3 then they are in thermal equilibrium with each other.” Results in the idea that there is something you could measure separately about S1 and S2 which would be the same. This “something” is temperature. The concept of temperature Look at the website and copy “The temperature connection” to your notes. Temperature is a variable of state . - it is a physical property related to the kinetic and potential energies of the atoms and molecules in a system. - it is measured using a thermometric scale which has one or more fixed reference points. Department of Physics Introduction IX The concept of temperature / contd. U is the internal energy of the system Infra-red (IR) U1 which is the sum of the translational, vibrational and rotational energies of its components (we will return to this later). If, for example, we bombard an isolated system with IR then: - its internal energy increases through the addition of heat Q T2 T1 T1 +Q U 2 U1 U2 T2 - its temperature increases The temperature of a system is only dependent on its internal energy Department of Physics Temperature and Heat I Young and Friedman (Y & F) Ch. 17 Thermometry - measurement of temperature. Consider 3 systems S1, S2, and S3. Let S3 have some observable property which scales (ideally linearly) with temperature. If S3 is placed in contact with S1 and then with S2 and the observable does not change, then S1 and S2 have the same temperature. S3 is a thermometer. Suppose that the property is X. Then, we would like: where X0 and c are constants. X T X 0 cT Need two fixed reference points to find X0 and c - i.e. for calibration. Department of Physics Temperature and Heat II Thermometry / contd. The two fixed points should be easy to reproduce, e.g.: - Ice point : liquid and solid water in equilibrium at 1 Atmosphere define as 0 on Celsius scale - Steam point : liquid water and water vapour in equilibrium at 1 Atmosphere define as 100 on Celsius scale Measure X at each fixed point then Department of Physics T 100 X X ice o C X steam X ice Temperature and Heat III Thermometry /contd. Examples of X - expansion of solids or liquids ~ cT (e.g. mercury thermometer) V V0 1 T 1T 2 2T 3 ... where V0 is volume at some “zero” temperature, is the volume coefficient of expansion, and T is temperature. V V V0 V0 T to first order (differentiate) - change in electrical resistance (e.g. thermistor, platimum resistance thermometer) R R0 1 T 1T 2 2T 3 ... hence (to first order) Department of Physics R R0 T Temperature and Heat IV Thermometry /contd. - Seebeck effect (thermocouple) (potential difference across a junction between dissimilar metals) T2 metal 1 (e.g. chromel) metal 2 (e.g. alumel) T1 = reference temperature T1 0 o C T1 0 o C T2 = temperature to measure V 1 70 VK -1 Reference junctions usually done electronically these days. Department of Physics Temperature and Heat IV Thermometry /contd. - Measurement of the wavelength of emitted em radiation (pyrometer) (Can be used remotely - e.g. for stars) Based on the Wien displacement law: mT 2.9 10 3 where m is the wavelength of at the peak of the spectral emittance curve for a black body Read section 39.5 (Continuous Spectra) in Y & F and copy fig 39.32 (Spectral emittance) into your notes Department of Physics mK Temperature and Heat V Thermometry /contd. - pressure of a gas (e.g. constant volume gas thermometer) based on the ideal gas equation pV nRT where n is the number of moles of gas and R is the universal gas constant use He at low pressure to get ideal behaviour Open to atmosphere Constant temperature bath h Fixed point p p h at Hg Gas at temperature T Flexible connection Department of Physics p T Temperature and Heat VI Thermometry /contd. Absolute zero and the constant volume thermometer Series of straight lines for different n extrapolate to a common point absolute zero temperature p n1 nR p T V n2 n3 o absolute zero 273.15 C 0 K -273.15 0 T / ºC need only 1 fixed reference point Department of Physics 100 Temperature and Heat VII Absolute zero / contd. Reference point: triple point of water (solid/liquid/vapour all in equilibrium at 0.01 ºC and 610 Pa) Ttr 273.16 K Then, where ptr is the pressure of the gas at Ttr in the gas thermometer Note: pressure of the gas in the thermometer at, Ttr not pressure of the equilibrium mixture whose temperature is being measured. Effect of non-ideality of gas on measurement of steam point: T / K 273.16 Lim ptr 0 p ptr p/MPa 0.08 H2 He Air O2 He at low pressure approaches the ideal behaviour T/K 373.15 Department of Physics 373.5 Temperature and Heat VIII Gas thermometer - worked example (Y & F17.8) A gas thermometer registers an absolute pressure corresponding to 325 mm Hg when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point? p const. T ptr pbp Ttr Tbp pbp Tbp ptr Ttr 373.15 325 273.16 444 mm Hg Department of Physics N.B. Use Kelvin scale for almost all thermodynamic calculations!