The Second And Third Law

Question 1

What is the difference between a spontaneous and non-spontaneous change?

Answer 1

Spontaneous change has the tendency to occur without work having to be done to bring it about. Non-spontaneous changes can only be brought about if work is done.

‘Spontaneous’ has nothing to do with speed in thermodynamics, it is to do with the tendency of a system to move towards lower energy.

Question 2

What is entropy?

Answer 2

It is the measure of disorder used in thermodynamics, S. this applies to both matter and energy.

Question 3

What is the second law of thermodynamics?

Answer 3

“The entropy of an isolated system tends to increase”

Question 4

What is the change of entropy by definition?

Answer 4

dS = dq(rev) / T
(rev) means reversible

The change in entropy of a substance is equal to the energy transferred as heat to it reversibly divided by the temperature at which the transfer takes place.

Question 5

What equation gives the change in entropy for the isothermal expansion of an ideal gas?

Answer 5

∆S = q(rev) / T
q(rev) = nRT ln Vf / Vi

Hence ∆S = nR ln Vf / Vi

Question 6

If the final volume is greater than the initial for the isothermal expansion of an ideal gas, what does this mean for the entropy of the system?

Answer 6

∆S = nR ln Vf / Vi

If Vf > Vi then the logarithm is positive, so ∆S is positive - meaning entropy increases as volume increases.

Question 7

Is entropy dependent on the temperature at which isothermal expansion occurs at?

Answer 7

No, it is independent of the temperature.

Question 8

Is entropy a state function? What does this mean for ∆S?

Answer 8

Yes, hence its value is independent of the path taken from the initial to final states.

This means that despite using a reversible path to calculate ∆S, the same value applies to an irreversible change between the two states.

Question 9

How can Pi / Pf = Vf / Vi

Answer 9

Pi Vi = nRT
Pf Vf = nRT

Hence Pi Vi = Pf Vf
Therefore Vf / Vi = Pi / Pf

Question 10

How is change in entropy and heat capacity related?

Answer 10

dS = q(rev) / T
C = q(rev) / dT

Hence dS = C/T dT

Question 11

How do you find change in entropy when heat capacity is constant?

Answer 11

dS = CdT / T

Once integrated ∆S = C ln(Tf / Ti) with limits Tf and Ti respectively.

Question 12

How is energy transferred as heat when a substance is at its melting or vaporisation temperature?

Answer 12

Reversibly

Question 13

What equation gives the entropy of fusion at constant pressure?

Answer 13

∆fusS = ∆fusH / Tf

(Tf = melting temperature)

Remember at constant pressure ∆H = q

Question 14

What equation gives the entropy of vaporisation at constant pressure?

Answer 14

∆vapS = ∆vapH / Tb

(Tb = boiling temperature)

Remember at constant pressure ∆H = q

Question 15

What is Trouton’s rule?

Answer 15

The entropy of vaporisation per one mole at the boiling temperature is the same for all liquids - except when specific intermolecular interactions are present, such as water.

Hence all liquids have approximately the same entropy of vaporisation at their boiling points

Question 16

What is the entropy of all perfectly crystalline structures at T = 0K?

Answer 16

0JK-1mol-1

Question 17

How are entropy changes in the surroundings calculated?

Answer 17

Since surroundings are so vast, they remain at constant pressure.

∆Ssur = q(sur,rev) / T

At constant pressure;
q(sur,rev) = ∆Hsur

Enthalpy is the same regardless of how heat is transferred, as it’s a state function.

If q(sur) = -q then;
∆Ssur = -q / T

This applies whether or not the process in the system is reversible.

Question 18

What equation gives the entropy changes in surroundings? (Constant pressure)

Answer 18

∆Ssur = -∆H / T

Question 19

What happens to entropy chengsin the surroundings if a process is exo/endothermic?

Answer 19

If exothermic; ∆H < 0 so ∆Ssur > 0.

If endothermic; ∆H > 0 so ∆Ssur < 0.

Question 20

What is the third law of thermodynamics?

Answer 20

The entropies of all perfectly crystalline substances are the same at T=0K

This is taken to be zero for convenience.

Question 21

For a spontaneous change, what must ∆Stotal be greater than?

Answer 21

∆Stotal > 0

∆Stotal = ∆S + ∆Ssur

Question 22

What is the total entropy change of a system and its surroundings at constant temperature and pressure?

Answer 22

∆Stotal = ∆S - ∆H/T

Question 23

What equation gives the Gibbs free energy at constant temperature? How is this derived?

Answer 23

∆G = ∆H - T∆S

Question 24

In a spontaneous change at constant temperature and pressure, what happens to the Gibbs energy?

Answer 24

The Gibbs energy decreases