Thermodynamics

Question 1

What is the first law of thermodynamics?

Answer 1

Energy can’t be created or destroyed
dU = dq + dw

Question 2

What is the second law of thermodynamics?

Answer 2

Entropy of an isolated system always increases

Question 3

What is the third law of thermodynamics?

Answer 3

Entropy of a system approaches a constant as temperature approaches absolute zero

Question 4

What is the difference between extensive and intensive variables?

Answer 4

Extensive: Depends on the size of system (n, m, V)
Intensive: Doesn’t depend on size of system (T, P, molar volume)

Question 5

What is the zeroth law of thermodynamics?

Answer 5

Two systems in equilibrium with a third system ar in thermal equilibrium with each other

Question 6

What is the ideal gas law?

Answer 6

PV = nRT

Question 7

What is Dalton’s Law?

Answer 7

Pi = XiP

Partial pressure of one component is the component fraction of the total pressure

Question 8

What is work? Is it path dependent?

Answer 8

dw = -p_ext * dV

It is path dependent

Question 9

What is heat?

Answer 9

Quantity that goes in / out of system that changes temperature of the system.

It is also path dependent

Question 10

What is heat capacity?

Answer 10

C = dq/dT –> how change in heat leads to change in temperature

Question 11

What is enthalpy?

Answer 11

Change in heat at constant pressure.

q = deltaH = U+pV

Question 12

What is entropy?

Answer 12

Delta S = integral of dq/T

reversible process = entropy is 0
irreversible process = entropy is less than 0

Question 13

What is the Carnot Cycle and its efficiency?

Answer 13

E = 1-Tc/Th

Essentially transferring heat from a hot sink to a cold sink and using that energy to do work

Question 14

Fundamental Equations of Thermodynamics

Answer 14

dU = TdS - PdV
dH = TdS + VdP
dF = -SdT - PdV
dG = -SdT + VdP

Question 15

What is the point of free energies?

Answer 15

Equations that minimize internal energy and maximize entropy

Question 16

What is Hemholtz Free Energy?

Answer 16

F = U - TS
relevant for constant T, constant V

Question 17

What is Gibb Free Energy?

Answer 17

G = U + PV - TS
relevant for constant T, constant P

Question 18

What is chemical potential?

Answer 18

How G changes when add or subtract certain amount of a component. Driving force of reaction

mu = dG/dn = dF/dn = dH/dn = dU/dn

also thought of as molar Gibbs Free energy

nmu = G

Question 19

Degree of freedom in phase diagrams?

Answer 19

point = 0df
line = 1df
phase = 2df

Question 20

What is the Clausius-Clapeyion Equation?

Answer 20

Relates slope of P vs. T phase line with other variables
(dP/dT)_coexist = (Delta S/Delta V) = (Delta H/ T* Delta V)

entropy vs. volume equation more relevant. Think about how changing phases will impact these variables

Question 21

Why is slope of PvT diagram of water have a negative slope?

Answer 21

From Clausius-Clapeyion, we usually get positive slopes. However, water expands when forming to solid, so slope is negative

Question 22

What is Gibbs Phase Rule?

Answer 22

F = degrees of freedom - how many variables need to know to define a system
C = number of components
P = number of phases

F = C-P+2

For solids, P not a variable, so
F = C-P+1

Question 23

What is the Ideal Model for Mixtures? What is the specific Law? Draw it

Answer 23

Both components are non-reacting and non-interacting

Follows Rauolt’s Law: P_A ~ 1-X_A
For when there is liquid phase of A and B, A is volatile and B is non-volatile. What is the vapor pressure of A at different concentrations of B?

Graph: When there is no X_B, vapor pressure of A is P_A*. As we increase B, P_A decreases linearly to 0 at X_B=1

Question 24

What is the Molar Gibbs Free Energy for an Ideal Mixture?

Answer 24

mu_A = mu_A* + RTlnX_A

When X_A<1, chemical potential decreases, G decreases – this is because there is more entropy in a mixed system

Question 25

What is the Gibbs Free Energy of Mixing 2 idea solutions of components A and B? What does it look like

Answer 25

DeltaG_mix = nRT(X_AlnX_A + X_BlnX_B)

Curve looks like a U

Question 26

What is the difference between ideal solutions and non-ideal solutions?

Answer 26

Ideal solutions: A&B don’t interact, don’t see each other

Non-ideal solutions: Interactions between AA, BB and AB

Question 27

What does “positive deviations” and “negative deviations” mean? What equation is used to determine this?

Answer 27

DeltaU = 2U_AB - (U_AA + U_BB)

Positive deviation = DeltaU > 0, so mixing is not favorable. A and B repulse each other. In P vs. X diagram, curves upward since molecules have increased pressure since they are repulsive

Negative Deviation = DeltaU < 0, A and B have slight attraction towards each other. In P vs. X diagram, curves downward since molecules have decreased pressure since they are attractive

Question 28

What are the two laws we use at dilute limits in non-ideal solutions?

Answer 28

When X_B –> 1, mostly see other B molecules, so we can model this as ideal. Use Raoult’s Law
P_B = X_BP_B*

When X_B –> 0, We use Henry’s Law. B mostly sees A molecules,

P_B = X_BK_B

K_B depends on if its a positive or negative deviation. KB higher than PB* if positive, lower if negative

Question 29

What are the 4 Colligative Properties?

Answer 29

1. Vapor Pressure Lowering (Roaoult’s Law)
2. Boiling Point Elevation
3. Freezing Point Depression
4. Osmotic Pressure

Question 30

What is Osmotic Pressure and its equation?

Answer 30

Osmotic Pressure is when you have a channel that is permeable to A and not B, very sensitive measurement that can be used to find molecular weight

Van Hoff Equation: piV = RTn
pi = osmotic pressure
n = moles of B

pi = rhogh
rho = density
g = gravity
h = height the liquid goes

Question 31

What is the thermodynamic activity?

Answer 31

activity is a measure of non-ideality.
a = P/P*
actual partial pressure / pure partial pressure

for Raoult’s Law, a = X
for Henry’s Law, a = kX

Question 32

What is the activity coefficient?

Answer 32

activity coefficient = a/X

=1, ideal solution
>1, positive deviation
<1, negative deviation