PHYSICS 231 Lecture 23: Temperature Remco Zegers Walk-in hour: Tue 4-5 pm Helproom PHY 231

quiz A boat carrying a large rock is floating on a lake. The rock is thrown overboard and sinks. The water level in the lake (with respect to the shore) rock >> water rises drops remains the same rock in boat: B=Mg Vdispl  waterg =(Mboat+Mrock)g Vdispl=(Mboat+Mrock)/water =Mboat/water+Mrock/water rock overboard: boat: Vdispl=Mboat/water rock under water: Vrock=Mrock/rock <<Mrock/water so lower total displaced volume PHY 231

Kinetic energy ~ T Chapter 10 Temperature Potential Energy -Emin R -Emin R The curve depends on the material, e.g. Emin is different for water and iron R 2 atom/molecules PHY 231

Solid (low T) Kinetic energy ~ T Potential Energy Rmin R -Emin R -Emin The temperature (and thus kinetic energy) is so small that the atoms/molecules can only oscillate around a fixed position Rmin PHY 231

Liquid (medium T) Potential Energy Kinetic energy ~ T Rmin R -Emin R -Emin On average, the atoms/molecules like to stick together but sometimes escape and can travel far. PHY 231

Gas (high T) Kinetic energy ~ T Potential Energy Rmin -Emin R -Emin R The kinetic energy is much larger than Emin and the atoms/molecules move around randomly. PHY 231

What happens if the temperature of a substance is increased? Rmin=Rave(T=0) Kinetic energy ~ T Rave(T>0) > Rmin T>To: The average distance between atoms/molecules is larger than Rmin: the substance expands R T=0: Average distance between atoms/molecules: Rmin -Emin PHY 231

Temperature scales Conversions Tcelsius=Tkelvin-273.5 Tfahrenheit=9/5*Tcelcius+32 We will use Tkelvin. If Tkelvin=0, the atoms/molecules have no kinetic energy and every substance is a solid; it is called the Absolute zero-point. Celsius Fahrenheit Kelvin PHY 231

Thermal expansion L=LoT A=AoT =2 V=VoT =3  length L L=LoT surface A=AoT =2 volume V=VoT =3  L0 : coefficient of linear expansion different for each material Some examples: =24E-06 1/K Aluminum =1.2E-04 1/K Alcohol T=T0 T=T0+T PHY 231

Water: a special case Coef. of expansion is negative: If T drops the volume becomes larger Coef. Of expansion is positive: if T drops the volume becomes smaller Ice is formed (it floats on water) PHY 231

Ice  (g/cm3) liquid 1 Phase transformation 0.917 ice Ice takes a larger volume than water! PHY 231

water=1000 kg/m3, so 1 liter is M=1 kg. ice=917 kg/m3=M/Vice=1/Vice expanding ice Someone puts a bottle of water of 1 liter (1E-03 m3) in the freezer. If there is 25cm3 space left in the bottle without water, what will happen when it freezes? water=1000 kg/m3, so 1 liter is M=1 kg. ice=917 kg/m3=M/Vice=1/Vice Vice=1/917=1.09E-03 m3=1.09E+03 cm3 (10% larger!). The volume becomes 90cm3 larger, but only 25cm3 is left. The bottle will break. PHY 231

Thermal equilibrium Thermal contact High temperature Low temperature High kinetic energy Particles move fast Low temperature Low kinetic energy Particles move slowly Transfer of kinetic energy Thermal equilibrium: temperature is the same everywhere PHY 231

Zeroth law of thermodynamics If objects A and B are both in thermal equilibrium with an object C, than A and B are also in thermal equilibrium. There is no transfer of energy between A, B and C PHY 231

Thermal expansion: an example In the early morning (T=30oF=272.4K) a person is asked to measure the length of a football field with an aluminum measure and finds 109.600 m. Another person does the same in the afternoon (T=60oF=289.1K) using the same ruler and finds 109.556 m. What is the coefficient of linear expansion of the ruler? L=LoT so = L/(L0T) T=16.7K L0=109.60 L=109.644-109.600=0.044 So: =24E-06 1/K The ruler has become larger by 0.044 m, so the person measures a length smaller by the same amount PHY 231

A heated ring A metal ring is heated. What is true: The inside and outside radii become larger The inside radius becomes larger, the outside radius becomes smaller The inside radius becomes smaller, the outside radius becomes larger The inside and outside radii become smaller PHY 231

Demo: bimetallic strips top bottom Application: contact in a refrigerator top<bottom if the temperature increases, The strip curls upward, makes contact and switches on the cooling. PHY 231

Demo’s Bimetallic coil Expanding and contracting rod PHY 231