Adiabatic Processes

Pressure/Temp and Vol/Temp

Adiabatic Compression If I compress air at atmospheric pressure and room temperature by a factor of 10 the temperature will go up by 1. Less than 10 degrees C 2. Between 10 and 50 degrees C 3. Between 50 and 100 degrees C 4. More than 100 degrees C

Blow on your hand

Malachi 2:10 Have we not all one father? hath not one God created us? why do we deal treacherously every man against his brother, by profaning the covenant of our fathers?

The first law of thermodynamics ∆E int = Q + W The internal energy of an ideal gas depends only on the temperature of the gas. Change of internal energy = heat put into system + work done on system

For an ideal gas... Always!!!!!

Deriving the Adiabatic Equation i.e. Going way beyond what you need to know for the homework and exams because you will hopefully learn something and, with luck, gain a greater appreciation of the power of differential calculus...

Three things changing, but in a defined way such that if I know how one changes, I should know others. To get rid of an unknown, I need another equation – here it is! But I need to write it in terms of P, V, and T. And what do I do with the integral in it? If I have a piston whose location is x, or a balloon with a radius x, or a basketball being squished into the floor by an amount x, I should be able to tell you any one just in terms of initial conditions and x. How do things change with x?

They each only have one “T” thing (P and V show up twice, as P and dP, V and dV, in the left equation), so that’s the easy one to solve for and eliminate. Take all the constants to one side and simplify. Then to keep things tidy, call it gamma.

Get P stuff on one side, V on other, integrate. Remember, when V is equal to its initial value, P is equal to its initial value. When V is its final value, P is its final value.

The path shown below is isothermal (ΔT= 0). The change in internal energy of the gas is A. Positive B. Negative C. zero P V

The path shown below is isothermal (ΔT= 0). The heat flow is A. Into the gas B. Out of the gas C. zero P V

The path shown below is adiabatic (Q = 0). The change in internal energy of the gas is A. Positive B. Negative C. zero P V

The two lines below represent an isotherm and an adiabat. Which one is the isotherm? A. The upper one B. The lower one P V

The two lines below represent an isotherm and an adiabat. Which one is the isotherm? A. The upper one B. The lower one P V