First Law

Question 1

First Law of Thermodynamics

Answer 1

dU = dQ + dW

U = internal energy
Q = heat
W = work

Question 2

Helmholtz Energy

Answer 2

ΔF = ΔU + TΔS

Question 3

How does thermodynamics describe the world?

Answer 3

separates the world into the system and the surroundings

Question 4

Isolated System

Answer 4

-doesn’t exchange energy or matter with the surroundings

Question 5

Closed System

Answer 5

-exchanges energy but not matter with the surroundings

Question 6

Open System

Answer 6

-exchanges energy and matter with the surroundings

Question 7

State Variables

Answer 7

T, V, P, U

Question 8

State Functions

Answer 8

-functions of state variables

Question 9

Extensive Variables

Answer 9

-depend on the size of the system, e.g. U, Nk

Question 10

Intensive Variables

Answer 10

-specify a local property independent of the size of a system e.g. T, P

Question 11

Zeroth Law of Thermodynamics

Answer 11

• if 2 systems are in thermal equilibrium with a third then they are also in equilibrium with each other
• there is a single property, temperature, that is common to all three systems and serves to indicate that they are in thermal equilibrium

Question 12

First Law

Answer 12

-when a system undergoes a change of state, the sum of the different energy changes (heat exchanges, work, etc.) is independent of the manner of the transformation and depends only on the initial and final states of the system:
B,A ∫ dU = Ub - Ua
OR for a cyclic process:
∮ dU = 0

Question 13

Perpetual Motion of the First Kind

Answer 13

• it is not possible either by mechanical, thermal, chemical or other devices to obtain perpetual motion
• i.e. it is impossible to construct an engine that will work in a cycle and produce continuous work or kinetic energy from nothing

Question 14

First Law

Closed System

Answer 14

dU = dQ + dW

dU = energy exchanged with thermal reservoir

Question 15

First Law

Open System

Answer 15

dU = dQ + dW + dUmatter

Question 16

Types of Work

Extension, Surface Expansion, Externsion

Answer 16

Extension: dW = Fdl
F = tension, l = length
Surface Expansion: dW = γdA
γ = surface tension, A = area
Expansion: dW = PdV
P = external pressure, V = volume 

-all are a product of an intensive factor and an extensive factor

Question 17

Types of Work

Electrical, Magnetic

Answer 17

Electrical: dW = ϕdQ
ϕ = potential difference, Q = charge
Magnetic: dW = -BdM
B = magnetic field, M = change in magentic dipole moment

Question 18

Work Done During any Infinitesimal Change in Volume

Answer 18

dW = -Pex dV

Pex = external pressure

Question 19

Reversible Change

Answer 19

Pex is always matched to Pint

Question 20

Irreversible Change

Answer 20

Pex is less than the internal pressure

Pex

Question 21

Isothermal Expansion of an Ideal Gas

Answer 21

T = constant
dU = dQ + dW = 0
dQ = -dW

-energy that enters the system as heat, leaves as work

Question 22

Adiabatic Expansion of an Ideal Gas

Answer 22

dQ = 0
dU = dQ + dW = dW

-change in internal energy is equal to the work done

Question 23

Ideal Gas Assumptions

Answer 23

1) particles do not interact (except through collisions), it doesn’t matter how close two particles get their potential energy is the same, this breaks down at high pressure as in reality all substance experience van der Waal’s interaction
2) particles do not take up any volume

Question 24

Calculating Heat Capacity

Finding an Expression for Heat

Answer 24

dU = dQ + dW
dQ = dU - dW
=dU + PdV
= δU/δT|v dT + δU/dV|t dV + PdV
=δU/δT|v dT + (δU/δV|t + P)dV

Question 25

Calculating Heat Capacity

Constant Volume

Answer 25

-start with the expression for heat:
dQ = δU/δT|v dT + (δU/δV|t + P)dV
-at constant volume, dV=0 so:
dQ = δU/δT|v dT
Cv = dQ/dT
Cv =  δU/δT|v

Question 26

Calculating Heat Capacity

Constant Pressure

Answer 26

start with the expression for heat:
dQ = δU/δT|v dT + (δU/δV|t + P)dV
Cp = dQ/dT |p
Cp = δU/δT|v + (δU/δV|t + P) dV/dT

Question 27

Calculating Heat Capacity

Difference in Cp and Cv for all substances

Answer 27

Cp - Cv = δU/δT|v + (δU/δV|t + P) dV/dT - δU/δT|v

= (δU/δV|t + P) dV/dT

Question 28

Classical Equipartition Theorem

Answer 28

-every degree of freedom contributes 1/2kT to the internal energy of the system

Question 29

Gamma

Answer 29

γ = Cp/Cv

for a monoatomic gas γ=5/3
for a diatomc gas γ=7/5

Question 30

Application of the First Law - Speed of Sound

Answer 30

-due to the rapid nature of pressure changes that propagate sound, hardly any heat is exchanged - appro. adiabatic
-speed of sound in medium depends on its bulk modulus and density Vs = √(B/ρ)
-bulk modulus B = γP
-for an ideal gas:
P = nRT/V = nM/V * RT/M = ρ RT/M
B = γρRT/M
Vs = √(B/ρ) = √(γRT/M)

Question 31

Calculating Heat Capacity

Difference in Cp and Cv for an Ideal Gas

Answer 31

starting with the general expression:
Cp - Cv = (δU/δV|t + P) dV/dT

-for an ideal gas:
PV=nRT so V = nRT/P and dV/dT = nR/P

Cv - Cp = (δU/δV|t + P) * nR/P
-for an ideal gas, internal energy doesn’t depend on volume so, δU/δV|t=0

Cv - Cp = P * nR/P = nR

Question 32

Reversible or Quasistatic Processes

Answer 32

• idealised processes that take place infinitely slowly in such a way that the system is always in equilibrium at every stage
• no real thermodynamic changes are quasistatic due to friction etc.
• BUT properties of state functions (that they only depend on the initial and final state not the path taken) allow us to define a quasistatic path between to states in order to calculate thermodynamic potentials of the initial and final states that will be the same for the actual path taken