Announcements 9/20/10
Demo: constant volume change (hopefully working today)
Do this “Quick Writing” assignment while you’re waiting:
Ralph is confused because he knows that when you compress gases, they tend to heat up (think of bicycle pumps). So, how are “isothermal” processes possible? How can you compress a gas without its temperature increasing?
Thought question (ungraded)
How will the temperature of the gas change during this process from A to B?
a. Increaseb. Decreasec. First increase, then
decreased. First decrease, then
increasee. Stay the same
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Pre
ssur
e (a
tm)
Volume (m3)
A
B
Reading quiz (graded)
What is “CV”?
a. heat capacity b. mass-pacityc. molar heat capacityd. molar heat capacity, but only for
constant volume changese. a detailed resumé
Thought question (ungraded)
Which should be larger, the molar heat capacity for constant volume changes or the molar heat capacity for constant pressure changes? (Hint: Think of the First Law.)
a. constant volumeb. constant pressurec. they are the samed. it depends on the temperature
CV and CP
Constant volume change (monatomic):W = 0Eint = Qadded
(3/2)nRT = Qadded
Compare to definition of C: Qadded = nCVT
(like Qadded = mcT)
CV = (3/2)R Constant pressure change
a. What’s different?b. result: (monatomic) CP = (5/2)R
What would be different for gases with more degrees of freedom?
Reading quiz (graded)
What does gamma equal in the equation for an adiabatic process:
a. CP + CV
b. CP - CV
c. CV - CP
d. CV / CP
e. CP / CV
constantPV
Isothermal vs Adiabatic
Isothermal: Adiabatic:
steeper curves for adiabatic
constantPV constantPV
Thought question
How much do you think the temperature of the air in this room would change by if I compressed it adiabatically by a factor of 10? (Vf = V0/10)
a. less than 0.1 degree Cb. about 0.1 degrees Cc. about 1 degree Cd. about 10 degrees Ce. more than 10 degrees C
Demo/Video
Video: adiabatic cotton burner Demo: freeze spray Video: adiabatic expansion
Derivation of PV (for Monatomic)Eint = Qadded + Won
(3/2) nRT = -integral(PdV)(3/2) nRdT = -PdV(3/2) nR d(PV/nR) = -PdV(3/2) (PdV + VdP) = -PdV(3/2) VdP = -(5/2) PdVdP/P = -(5/3) dV/VlnP = (-5/3)lnV + constantlnP = ln(V-5/3) + constantP = constant V-5/3 (it’s a different constant)
P V5/3 = constant
What’s differentif diatomic?
Thought question Which of the curves on the PV diagram below
is most likely to represent an isothermal compression, followed by an adiabatic expansion back to the initial volume?
a.
b.
c.
d.
e.
Thought questions What would be the molar specific heat for an
adiabatic process? (Hint: think of Q = nCT.)a. CV
b. CV + Rc. CV + 2Rd. CV - Re. none of the above
What would be the molar specific heat for an isothermal process? (Same hint.)
a. CV
b. CV + Rc. CV + 2Rd. CV - Re. none of the above
Water/steam “saturation curve”: ideal gas?
0.00 0.01 0.02 0.03 0.04 0.05 0.060
5000
10000
15000
20000
25000
30000
Part Liquid, Part GasAll Liquid
Pre
ssu
re (
kPa
)
Volume, divided by mass (m3/kg)
bk = actual data for water/steam
All Gas
adding heatenergy, T=325C
1 atm= 101 kPa
Water/steam “saturation curve”: ideal gas?
0.00 0.01 0.02 0.03 0.04 0.05 0.060
5000
10000
15000
20000
25000
30000
Part Liquid, Part GasAll Liquid
Pre
ssu
re (
kPa
)
Volume, divided by mass (m3/kg)
bk = actual data for water/steamrd = ideal gas, T=400bl = ideal gas, T=500gn = ideal gas, T=600
All Gas
adding heatenergy, T=325C
1 atm= 101 kPa
Water/steam “saturation curve”: ideal gas?
0.00 0.01 0.02 0.03 0.04 0.05 0.060
5000
10000
15000
20000
25000
30000
Part Liquid, Part GasAll Liquid
Pre
ssu
re (
kPa
)
Volume, divided by mass (m3/kg)
bk = actual data for water/steamrd = ideal gas, T=400bl = ideal gas, T=500gn = ideal gas, T=600
All Gas
"critical point"
adding heatenergy, T=325C
1 atm= 101 kPa
Water/steam “saturation curve”: ideal gas?
0.00 0.01 0.02 0.03 0.04 0.05 0.060
5000
10000
15000
20000
25000
30000
Part Liquid, Part Gas
????
All Liquid
Pre
ssu
re (
kPa
)
Volume, divided by mass (m3/kg)
bk = actual data for water/steamrd = ideal gas, T=400bl = ideal gas, T=500gn = ideal gas, T=600
All Gas
"critical point"
adding heatenergy, T=325C
1 atm= 101 kPa
