First Law of Thermodynamics Physics 202 Professor Lee Carkner Lecture 11

PAL #10 Temperature  How does the Galileo thermometer work?   The water in the tube changes density with T   Water gets less dense as T rises and so the balls fall (64 to 80)  Heat Al until it floats  Need  = 1000 kg/m 3 so V = m/  = 2700/1000 = 2.7     V = V  DT,  T =  V/V  = 1.7/((1)(6.9X10 -6 )) = C   Al would melt before getting to this temperature

Heat Capacity   Put a wooden spoon in a pot of water and boil it   Heat capacity (unit energy per degree temp) is given by: Q = C (T f - T i ) = C  T  Where:  Q = heat (J)   C is a property of a specific object

Specific Heat  C=cm  Where m is the mass and c is the specific heat   Each type of substance has a c (e.g. water, iron, etc.)  Q = cm(T f - T i )  Amount of heat (Q) needed to change the temperature of m kg of a certain type of substance from T i to T f

Molar Specific Heat   One mole = 6.02 X atoms or molecules  Q = c mol (# of moles) (T f - T i )  Used for gas

Heat of Transformation   Boiling water stays at 100 deg C, the added energy goes into transforming the water from liquid to gas  Q = L m  Where L is the heat of transformation

Vaporization and Fusion  For the phase change from liquid to gas the heat of vaporization, L V is needed  For the phase change from solid to liquid the heat of fusion, L F is needed   The total heat necessary to change temperature and state is the sum of heats required for each

Phase Curve for Water

Calorimetry 1)Write out equation adding all heats in symbolic form and set equal to zero  e.g., Q 1 + Q 2 + Q 3 = 0 or m 1 c 1  T 1 + m 2 L 2 + m 3 c 3  T 3 =0 2)Substitute numbers, use correct values for c and L  3)Make sure units for m, c, L and T match  4)Always use  T = T f -T i (don’t add your own sign!)   Temperature decrease results in a negative loss of heat 5)For Lm, make positive if heat is absorbed and negative if heat is given off  Solve for required variable

Work and Internal Energy   No heat can travel in or out  If weight is removed from the piston head, the remaining weight will rise   Where does the energy come from?  It must come from the internal energy of the gas  Internal energy depends on temperature

Work and Heat   The thermal reservoir can add or subtract heat from the system   What happens to the internal energy of the system as heat is applied or work is done?

The First Law of Thermodynamics   This conservation of energy is called the First Law of Thermodynamics  E int =  Q -  W   Sign convention:  If work is done by the system  W is positive, if work is done on the system  W is negative

Work, Pressure and Volume  How does work change the system?   The amount of work done in moving something a small distance ds is:  However, F = pA and dV = A ds  The total work is dW integrated over the volume change  W =  dW =  p dV (integrated from V i to V f )  Work is the area under the curve on a p-V diagram

p-V Diagrams

The p-V Curve  Pressure must be non-zero in order for work to be done   If the volume increases, work is done by the system and the work is positive   No volume change, no work  If the process is cyclical and returns to the same point by two different paths the area between the paths is equal to the work (and also equal to the heat)

Adiabatic  Q=0 so  E int = -W   Consider a thermally isolated (insulated) piston with weight on top   By changing the weight, the gas is compressed or expands

Constant Volume   E int = Q  If any heat is applied to the system it goes directly into internal energy   The gas cannot expand

Cyclical Process   The final pressure, volume and internal energy are the same as the initial  E int = 0 so Q=W  There are many different ways to produce a cyclical process 

Next Time  Read:

Which of the following places the temperatures in the correct rank, highest to lowest?  a) 50 X, 50 W, 50 Y  b) 50 X, 50 Y, 50 W  c) 50 W, 50 X, 50 Y  d) 50 Y, 50 W, 50 X  e) 50 Y, 50 X, 50 W

Consider 3 aluminum plates, plate A has area of 1X1 m, plate B has area of 2X2 m and plate C has area of 3X3 m. If the temperature of the plates is raised by 10 degrees, which plates has the greatest increase in area? a) A b) B c) C d) All tie e) You cannot tell with out knowing the thickness