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UH PHYS 1302 - Ch16

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Chapter 16 - Temperature and Heat1 Temperature and the Zeroth Law of Thermody-namicsHeat is the energy that is transferred between objects because of a temperature dif-ference.If heat can flow between two objects, they are in what is called “thermal contact.”Thermal contact is not the same as physical contact - heat can be transferred withouttwo objects physically touching. When objects are in thermal contact, the transferof heat stops when the objects are in “thermal equilibrium.” When two objects arein thermal equilibrium, they have the same temperature.Zeroth Law of Thermodynamics: If two objects are in thermal equilibrium witha third system, they are in thermal equilibrium with each other.2 Temperature ScalesCelsius: water freezes at 0◦C and boils at 100◦CFahrenheit: water freezes at 32◦F and boils at 212◦F.Conversion between Fahrenheit and Celsius:TF=95TC+ 32 (1)TC=59(TF− 32) (2)L. Whitehead 1 Phys 1302Convert 40◦C to Fahrenheit.TF=95(40) + 32 = 104◦FExperiments show that there is a lowest temperature below which it is not possibleto cool an object. This lowest temperature is called “absolute zero.” The pressureof a gas has a depends on its temperature. This relationship can be mapped out inthe lab for different gases. If you extrapolate the curve back to the point where thepressure of the gas would be zero, you find that zero pressure happens at the sametemperature for any gas. That temperature is defined as absolute zero.Kelvin: The Kevin scale is set so that 0 K is exactly absolute zero. The size of aKelvin degree is the same as the size of a Celsius degree, i.e. a change of 1 degreeKelvin is equivalent to a change of 1 degree Celsius.The conversion between Celsis and Kelvin:T = TC+ 273.15 (3)The degree symbol (◦) is not used with the Kelvin scale.What is absolute zero in degrees Fahrenheit?0 = TC+ 273.15TC= −273.15◦CTF=95(−273.15) + 32TF= −459.67◦F3 Thermal ExpansionMost materials expand when heated.L. Whitehead 2 Phys 1302A rod of length L0will expand by an amount proportional to the temperature changewhen heated or cooled. The length change depends on the coefficient of linear ex-pansion (α). α is different for different materials.∆L = αL0∆T (4)Steel rails for a train track are laid in a region subject to extremes of temperature.The rails are laid in sections that are 5.2 m long. How much longer is each sectionwhen the temperature is 50◦C compared to when to the temperature is -10◦C?The change in temperature is ∆T = 50.◦C − (−10◦C) = 60◦C = 60K∆L = αL0∆T= (12 × 10−6K−1)(5.2m)(60K)= 3.7 × 10−3m = 3.7 mmA bimetallic strip consists of two metals bonded together to form a linear strip. Twodifferent metals will generally have different coefficients of linear expansion. Whenthe strip is heated or cooled, one side of the strip will expand or contract more thanthe other. Thus the shape of the strip (the amount that is curves) depends on thetemperature. Many thermostats have a bimetallic strip to turn on or shut off a heater.If a metal square with side length L is heated, the area will expand:A0= (L + ∆L)(L + ∆L)= (L + αL∆T )(L + αL∆T )= L2+ 2(L)(αL∆T ) + (αL∆T )2= L2+ 2αL2∆T + α2L2∆T2L. Whitehead 3 Phys 1302For typical changes in temperature, α∆T is small, which means the term proportionalto α2∆T2is typically negligible. Let A = L2be the original area.A0≈ L2+ 2αL2∆TA0≈ A + 2αA∆TA0− A ≈ 2αA∆T∆A ≈ 2αA∆T (5)The above applies to any area, not just a square.What about a washer (a metal disk with a hole in the middle)? The hole actuallyexpands along with the washer (with the same coefficient of expansion).Similarly, the empty volume within a container expands when the container is heated.The change in volume is given by∆V = βV ∆T ≈ 3αV ∆T (6)where β is called the coefficient of volume expansion. β can be approximated byβ ≈ 3α.Suppose we heat a copper container (α = 17 × 10−6K−1) of volume 150 cm3that iscompletely filled with oil (β = 0.68 × 10−3K−1) by 10◦C. How much oil spills out?The volume of the copper container and the volume of oil both expand. If the volumeof the oil expands more than the volume of the container, oil will spill out. Theamount that spills will be the difference between the volume expansions. ∆T = 10◦CL. Whitehead 4 Phys 1302= 10 K.∆Vcopper= 3αV ∆T= (3)(17 × 10−6K−1)(150cm3)(10K)= 0.076cm3∆Voil= βV ∆T= (0.68 × 10−3K−1)(150cm3)(10K)= 1.02cm3Vspill= ∆Voil− ∆Vcopper= 0.94cm3The density of water (density is mass per volume) reaches a maximum at about 4◦C.That means if you heat water from 0 to 4◦C, it actually contracts (becomes moredense) instead of expanding. Above 4◦C, water expands with heating like any normalliquid.When temperatures drop in winter, the surface waters of a lake cool first and sink(because they become more dense as they get cooler). The warmer water rises tothe top and gets cooled. Eventually, all the water is about 4◦C. At that point, whenthe water gets cooler, it actually rises (becomes less dense). So after 4◦C, the coolestwater is on top, and the top of the lake freezes first. This creates an insulating layer,and the water at the bottom of the lake doesn’t freeze - it stays at about 4◦C. Ifwater didn’t have this property, lakes would freeze from the bottom up. If it wascold enough, the lake could freeze solid - meaning fish wouldn’t survive.L. Whitehead 5 Phys 13024 Heat and Mechanical WorkHeat is just another form of energy, and must be taken into account when applyingconservation of energy.One unit of heat is the calorie (cal); one kilocalorie (1 kcal = 1000 cal) was definedas the amount of heat it took to raise the temperature of 1 kg of water from 14.5◦C to 15.5◦C. The mechanical equivalent of heat (the equivalent mechanical work ofone calorie of heat transfer) is:1cal = 4.186J (7)The unit that you are familiar with from nutritional information is the Calorie (cap-ital C) which is equivalent to 1 kilocalorie (lowercase c).Another unit for measuring heat is British thermal units (Btu). 1 Btu is defined asthe energy required to heat 1 lb of water from 63◦F to 64◦F.1Btu = 0.252kcal = 1055J (8)Suppose a 65 kg person climbs 100 stairs, with each stair 20 cm high. How manycalories do you burn?The work you are doing against gravity is converted to heat energy. The total changein height is (20 cm)(100) = 2000 cm = 20 m.Q = U = mgh=


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UH PHYS 1302 - Ch16

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