2. 13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics Two objects in contact, at different temperatures, will have heat energy travel in both directions, but mostly, ‘downhill’ to the cooler object until they reach thermal equilibrium. The zeroth law of thermodynamics states that if two objects are in thermal equilibrium with a 3 rd system, then they are in equilibrium with each other.

3. 13-4 Thermal Expansion Most substances expand when they are heated and contract when they are cooled.  L=  L o  T c L= L o (1 +  T) …see page 388 for chart See Example 13-3  13-6 on page 389 …For volume expansion,  V=  V o  T c See Example 13-7 p390

4. 13-5 Anomalous Behavior of Water If water, at 0 0 C is heated it decreases in volume until it reaches 4 0 C See page 391 graph

5. 13-6 Thermal Stresses  L=  L o  T c  L=  F/A) L o  L o  T c =  F/A) L o So…F=  EA  T c See Example 13-8

6. 13-7 The Gas Laws and Absolute Temperature PV/T= (P 2 V 2 /T 2 ) …The combined gas law… PV= P 2 V 2 Boyle’s Law P/T= (P 2 /T 2 ) Gay-Lussac’s Law V/T= V 2 /T 2 Charle’s Law Use Kelvin temperature for all kinetic/gas problems

7. Homework P413-414 pr#9-13,24-25,28-30 due Friday BOP