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1. THERMODYNAMIC STATES AND THE FIRST LAW (1001-1030) 1001 Describe briefly the basic principle of the following instruments for making temperature measurements and state in one sentence the special usefulness of each instrument: constant-volume gas thermometer, thermo- couple, thermistor. ( Wisconsin) Solution: Constant-volume gas thermometer: It is made according to the princi- ple that the pressure of a gas changes with its temperature while its volume is kept constant. It can approximately be used as an ideal gas thermometer. Thermocouple thermometer: It is made according to the principle that thermoelectric motive force changes with temperature. The relation be- tween the thermoelectric motive force and the temperature is 8 = a + bt + ct2 + dt3 , where E is the electric motive force, t is the difference of temperatures of the two junctions, a,b,c and d are constants. The range of measurement of the thermocouple is very wide, from -2OOOC to 16OOOC. It is used a practical standard thermometer in the range from 630.74'C 1064.43"C. Thermister thermometer: We measure temperature by measuring the resistance of a metal. The precision of a thermister made of pure platinum is very good, and its range of measurement is very wide, so it is usually used as a standard thermometer in the range from 13.81K 903.89K. 1002 Describe briefly three different instruments that can be used for the accurate measurement of temperature and state roughly the temperature range in which they are useful and one important advantage of each in- strument. Include at least one instrument that is capable of measuring temperatures down to 1K. ( 3
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4 Problems d Sdutio~ on Thermodynamics tY Statistical Mechanics Solution: 1. Magnetic thermometer: Its principle is Curie's law x = C/T, where x is the susceptibility of the paramagnetic substance used, T is its absolute temperature and C is a constant. Its advantage is that it can measure temperatures below 1K. 2. Optical pyrometer: It is based on the principle that we can find the temperature of a hot body by measuring the energy radiated from it, using the formula of radiation. While taking measurements, it does not come into direct contact with the measured body. Therefore, it is usually used to measure the temperatures of celestial bodies. 3. Vapor pressure thermometer: It is a kind of thermometer used to measure low temperatures. Its principle is as follows. There exists a definite relation between the saturation vapor pressure of a chemically pure material and its boiling point. If this relation is known, we can determine temperature by measuring vapor pressure. It can measure temperatures greater than 14K, and is the thermometer usually used to measure low temperatures. 1003 A bimetallic strip of total thickness z is straight at temperature T. What is the radius of curvature of the strip, R, when it is heated to tem- perature T+AT?
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