THERMO5 Flashcards
How can you raise the temperature of a system?
- adding heat
- doing work on it
One Joule
Definition
-the mechanical (potential) energy required to raise the temperature of 1g of water by 1K
First Law of Thermodynamics
ΔEint = Qin + Won
ΔEint = increase in internal energy of the system Qin = heat transferred into the system Won = work done on the system
cv’
molar specific heat at a constant volume
cp’
molar specific heat at constant pressure
Ratio Between cv’ and cp’ as
cp’ > cv’ for substances that expand on heating since work is done against the surroundings during expansion
cp’ ≈ cv’ for liquids and solids as any expansion is very small
Determining Won
-for a gas exerting a force F on a piston surface area A, the work done by the gas to move the piston a distance dx is
dWby = Fdx = PAdx = PdV
-the work done on the gas is the negative of the work done by the gas
-so dWon = -Pdv, giving
Won = -∫P dv
Won
Constant Pressure
Won = -PΔV
Won
Constant Volume
Won = 0
First Law of Thermodynamics
Ideal Gas at Constant Volume
ΔEint = CvΔT
First Law of Thermodynamics
Ideal Gas at Constant Pressure
ΔEint = CpΔT - PΔV
Mayer’s Equation
Cp - Cv = nR
AND
cp’ - cv’ = R
Monatomic Gas
cv’
cv’ ≈ 1.5R
Diatomic Gas
cv’
cv’ ≈ 2.5R
Polyatomic Gas
cv’
cv’ > 2.5R
How to find cv’ for the general case
Cv = dEint/dT
and cv’ = Cv / n
What does internal energy in an ideal gas depend on?
only temperature
Joule Thompson Effect
Definition
a real gas cools when undergoing a free expansion
Joule Thompson Effect
Expansion of Ideal Gas into Vacuum
-gas allowed to freely expand into the vacuum in apparatus insulated from the surroundings
-when the gas reaches equilibrium the temperature is found to have remained for constant (for gases at low density)
-shows that internal energy does not depend on the volume of a ideal gas
KEav = 3/2 nRT
Joule Thompson Effect
Expansion of Real Gas into Vacuum
- real gases have attractions between molecules
- as the gas expands, the potential energy of the molecules is increased as they get further apart
- for a rigid insulated system this increase in PE can only come from reducing the KE
- so the temperature is reduced slightly
Heat Capacity Ratio
Equation
γ = Cp / Cv = cv’ / cp’
Monatomic Gas
Heat Capacity Ratio
γ = 5/3 ≈ 1.67
Diatomic Gas
Heat Capacity Ratio
γ = 7/5 ≈ 1.40
Polyatomic Gas
Heat Capacity Ratio
γ = 8/6 ≈ 1.33
