1. Thermal Expansion  Heating an object causes it to expand  Some objects expand more than others when heated  Heating a glass jar makes the lid easier to remove  The degree of expansion depends on the change in temperature and the coefficient of expansion

2. Thermal Expansion of Ruler

3. Linear Expansion  The degree to which the length of an object changes is given by:  L = L   T  Where  is the coefficient of linear expansion  This applies to all dimensions of a solid length, width and height  Example: bimetal strip  Two strips of metal with different coefficients of linear expansion attached together  As the strip heats up, one side expands more than the other bending the strip  This principle is used in dial thermometers and thermostats

4. Bimetal Strip

5. Volume Expansion  If the linear dimensions of a solid change then the volume must change:  V = V   T  Where  =3   If the volume changes with temperature but the mass stays the same, then the density must decrease  Density in general decreases with increasing temperature  This is what makes a hot air balloon work

6. Ideal Gas  One reason that we use the mole is that 1 mole of any gas will behave similarly  Specifically 1 mole of any gas held at constant temperature and constant volume will have the almost the same pressure  This strictly true only for low densities  Gases that obey this relation are called ideal gases  A fairly good approximation to real gases

7. Ideal Gas Law  The temperature, pressure and volume of an ideal gas is given by: pV = nRT  Where:  n is the number of moles  R is the gas constant 8.31 J/mol K  T must be in Kelvins

8. Mole  When thinking about molecules it sometimes is helpful to use the mole 1 mol = 6.02 X 10 23 units  6.02 x 10 23 is called Avogadro’s number (N A )  For a 1 mole sample the mass is given by the molar mass (M) M = mN A  Where m is the mass per molecule or atom  A mole of any gas occupies about the same volume  Gases with heavier atoms have larger molar masses

9. Isotherms  From the ideal gas law we can get an expression for the temperature PV = nRT T = PV/nR  For an isothermal process temperature is constant so: T = PV/nR = constant  If P goes up, V must go down  Can plot this on a PV diagram as isotherms  Lines of constant temperature  One distinct line for each temperature