Concept Map 4

Concept Map 4

1. Final Exam Review for Group 5B

2. Thermodynamics

   • Focuses on energy rather than forces as well as conservation of energy. Thermodynamics is the transfer of energy between systems of particles and is about the way changes in the energy of a system affects its properties. New quantities, such as temperature and heat, are needed to describe the properties of systems and their interactions.
     • System
       • A thermodynamic system contains multiple particles, usually a very large number. Systems are able to exchange energy with other systems.
         • Example: A balloon filled with oxygen molecules.
   • Temperature
     • Each system has its own temperature and T1>T2. System 1 is hotter than system 2 and if both are brought into contact, energy is spontaneously transferred from system 1 to system 2. Eventually, the two will have the same temperature and will have reached thermal equilibrium.
     • Heat
       • The energy that flows between the systems is called heat or heat energy. Heat is energy that passes from one system to another by virtue of a temperature difference. The terms heat and heat energy are used interchangeably. In physics, they always refer to the transfer of energy between systems.
         • The SI unit of heat is the same as for energy, the Joule (J) A unit called the calorie is widely used for heat. 1 cal=4.816 J. The calorie, with an uppercase "C" is used to measure the energy content of food. 1 Calorie=1000 calories
       • Heat Capacity
         • The ratio between the heat and energy added to a system and the resulting change in temperature. Heat capacity =Q/change in temperature
       • Specific Heat
         • Takes into account the size (mass) of the system. Specific Heat=c=Q/m*change in T
         • Q=mc*change in T
       • Calorimetry
         • Based on the principle of conservation of energy and can be used to find the specific heat of a system.
     • Tk=Tc+273.15 (From Celsius to Kelvin) The size of the temperature units are the same so a change of 1 degree on the Celsius scale is the same as the change of one kelvin on the Kelvin scale.
       • Tf=9/5 Tc+32 (from celsius to fahrenheit) The different sizes of the degree as well as different freezing points of water both have to be taken into account.
         • Example: The melting point of a certain substance is 177.9 degrees Celsius. What is the temperature of the Fahrenheit and Kelvin scales?

3. Chapter 14

4. Chapter 15

   • Avogadro's Number
     • 6.02 x 10^23
     • The atomic mass of an element is the mass of a natural sample of the element containing one mole of atoms.
       • m=M/Na
       • Ideal Gas Law
         • PV=nRT
           • All of the laws for a dilute gas are contained in a single relation called the ideal gas law.
           • R= 8.31 J/mol K and is called the universal gas constant. n is the number of moles of gas present.
         • The molecules in a gas move in all directions with different speeds. Look at one molecule colliding with a wall. Such collisions are elastic. From the Impulse Theorem, Change in P=F*change in T
           • Pressure
             • For an elastic collision, the sped before and after the collision will be the same and F=(2mv) /change in T. Looking at the molecules that strike the wall in a given period of time, Ftotal=(Nmv^2)/(3L) The pressure of F/A and the volume is LxA, so P=Nmv^2/3V and PV=N*mv^2/3
   • Kinetic Energy
     • 1/2mv^2
     • Boltzmann's Constant=3/2 kBT
       • The speed of a molecule can be found from the KE equations v= the square root of 3kBT/m
         • For air at room temperature, nitrogen molecules have a speed of approximately 516 m/s.
           • Example: What is the temperature of an ideal gas whose molecules have an average translational kinetic energy of 3.20 x 10^-20J?
     • Proportional to the temperature and this is how the macroscopic quantities in the ideal gas law are related to the microscopic quantities that appear in Newton's Laws.
   • Internal Energy
     • Depends only on the number of particle present and the temperature of the gas. In terms of moles, U=3/2 nRT. These results apply only to monatomic gases. In other materials, the contribution from potential energy becomes important.

5. Chapter 16

   • First Law of Thermodynamics
     • If an amount of heat,Q, flows into a system from its environment and an amount of work, W, is done by the system on its environment, the internal energy of the system changes by an amount. Change in U=Uf-Ui=Q-W
       • Positive Q indicates heat flows into the system and energy increases, change in U is positive.
       • Negative Q indicates heat flows out of the system and energy decreases, change in U is negative.
     • Example: Consider a flexible balloon containing n=3.5 moles of an ideal monatomic gas such as Helium. The balloon is placed over a flame so that Q=700 J of heat flows into the gas, and its temperature increases by 10K. How much work is done by the gas in the balloon on its environment during this process?
     • Example: A system takes in 4558 J of heat and does 3804 J of work on its surroundings. What is the change in the internal energy of the system?
     • Thermal Reservoir
       • A reservoir is much larger than the system to which it is connected. There is essentially no change in temperature of the reservoir when heat enters or leaves it. The notion of a thermal reservoir comes up often in discussions of thermodynamic processes.
     • Calculating Work
       • If F is the forces exerted by the gas on the piston, the work done by the gas on the piston is W=F*change in x. The piston is part of the environment of the gas. Work is done by the gas on the environment. If the pressure in the gas is P, and the area of the piston is A, then F=PA. The work is W=PA*change in x=P*change in V
       • W=P*change in volume=0
       • Many paths can connect the same initial and final states. Change in U is the same for any path that connects the same initial and final states. The amount of work depends on the path.
   • Isothermal Process(Constant Temperature)
     • An isothermal process is one with constant temperature. On a P-V diagram, an isothermal process is a curved line. Both pressure and volume may change. From the ideal gas law, P is inversely proportional to V.........W=nRTln(Vf/Vi)
   • Conclusions from Conservation of Energy
     • The internal energy of a system depends only on the current state of the system. Changes in the internal energy are thus independent of the path taken in a thermodynamic process. The change in internal energy depends only on the internal energies of the initial and final states. The work done during a thermodynamic process depends on the path taken. Even with the same initial and final states, two different thermodynamic paths can have different values of W.