Entropy and Temperature

Question 1

What is the equation for entropy?

Answer 1

S=k_BlnΩ
Ω is the no of microstates on the macrostate

Question 2

How does entropy relate to the number of microstates?

Answer 2

For more microstates the system is less defined and has greater entropy
Entropy is related to the disorder

Question 3

How does entropy combines in thermodynamics?

Answer 3

S_TOT=S₁+S₂

Question 4

How does entropy combines in SM?

Answer 4

Ω_TOT=Ω₁+Ω₂
S_TOT=S₁+S₂

Question 5

What is the condition for isothermal expansion?

Answer 5

dU=0

Question 6

What is the 2nd law for thermodynamics?

Answer 6

An isolated system in equilibrium is a state of maximum entropy

Question 7

What is the 2nd law for SM?

Answer 7

An isolated system in equilibrium will adopt the state with the highest number of microstates

Question 8

When is equilibrium reached?

Answer 8

When Ω_TOT is maximised
d(Ω₁Ω₂)/dE₁=0

Question 9

What is the statistical definition of temperature?

Answer 9

1/k_BT=dlnΩ/dE

Question 10

What is the 1st law?

Answer 10

dU=TdS-pdV

Question 11

What is the equation for temperature in thermodynamics?

Answer 11

1/T=(dS/dU)
At constant V

Question 12

What is the equation for temperature in SM?

Answer 12

1/T=dS/dE

Question 13

What is β?

Answer 13

β=1/k_BT

Question 14

What is the Boltzmann distribution?

Answer 14

P(E_i)=e^-βE/Z

Question 15

What is the partition function?

Answer 15

Z=Σe^-βE

Question 16

How do we measure entropy?

Answer 16

Measure changes in entropy using heat capacity

Question 17

What is the Gibbs’ Entropy Formula?

Answer 17

S=-k_BΣP_ilnP_i

Question 18

What is P_i for an isolated system in equilibrium?

Answer 18

P_i=1/Ω