Thermodynamics Cheat Sheet
Calorimetry
Heat required to change temperature: Q = mcΔT
Heat required to change phase: Q = mL
Ideal Gas Law: PV = nRT (in Kelvin)
|
Boyle's Law |
Constant Temperature |
PV = constant |
P1V1=P2V2 |
|
Charles/Gay Lussac Law |
Constant Pressure |
V/T = constant |
V1/T1=V2/T2 |
0th Law: Two objects, each in thermal equilibrium with a third object, are in thermal equilibrium with each other.
Math Example: If A = C and B = C, then A = B.
1st Law: The change in internal energy of a system equals the difference between the heat taken in by the system and the work done by the system. Formula: ΔU = Q - W (in Kelvin)
|
Adiabatic |
no heat flow |
Q = 0 |
ΔU = W |
|
Isothermal |
no temp change |
ΔT = 0 so ΔU = 0 |
Q = W |
|
Isochoric |
no volume change |
ΔV = 0 so W = 0 |
ΔU = Q |
|
Isobaric |
no pressure change |
ΔP = 0 |
W=PΔV |
2nd Law:
Clausius statement: Heat cannot, by itself, pass from a colder to a warmer body.
Kelvin-Planck statement: It is impossible for any system to undergo a cyclic process whose sole result is the absorption of heat from a single reservoir at a single temperature and the performance of an equivalent amount of work.
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Actual Thermal Efficiency |
Ratio of work to heat input |
Eff = W/QH |
|
Ideal Thermal Efficiency |
Best possible case |
Ideal Eff = 1-TC/TH |
|
Entropy |
How much energy/heat is unavailable for conversion into work |
ΔS = Q/T |
"Poker game" analogy of the three laws of thermodynamics
0th Law: You can't get out of the game (everything in the universe is in the system, so all objects are in thermal equilibrium or are moving towards it - unless we do something about it)
1st Law: You can't win (You can't get something for nothing. If you want work out, you must put heat/energy in and vice versa)
2nd Law: You always lose (Efficiency < 1, Entropy > 0)
WebLinks
http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon
Exercise
Consider
a system that is taken along the paths shown on the P-V diagram. Assume Ua
= 30,000 J
a) Find the work done by the system in going from a to b.
b) Find the work done by the system in going from b to c.
c) If 20 kJ of heat enters the system along the path from a to b, what is the internal energy at point b?
d) If the internal energy at point c is 95 kJ, how much heat enters or leaves the system along the path from b to c?
e) Run it backwards: If 21 kJ of heat enters the system in going from a to d, what is internal energy at point d?
f) Run it backwards: Find the heat that enters the system along the path from d to c.
g) If the system is taken along the closed loop a→b→c→d→a, how much work is done?
h) Find the area of the rectangular path.
i) What is the net heat that enters the system?