Chapter1 part B: Thermodynimcs fundamentals

Question 1

What are the units of:

1. Force
2. Pressure
3. Energy
4. Power

Answer 1

1. Force: kg*m/s² N
2. Pressure: kg/(m*s²) Pa
3. Energy: kg*m²/s² J
4. Power: kg*m²/s³ W

Question 2

What is the difference between an open and a closed system?

Answer 2

in open systems there is also a mass flow across the boundary

Question 3

How does power relate to work?

Answer 3

The power is the rate of work, It is the work generated over time:

P = 𝑑𝑊 𝑑𝑡 = 𝐹 ⋅ v

Question 4

State the first law of thermodynamics

Answer 4

“The first law of thermodynamics states that the overall energy of any closed system is conserved. No energy can be lost. This is equivalent to the energy balance.”

Question 5

State the second law of thermodynamics

Answer 5

The second law of thermodynamics introduces irreversibilities. Examples of such irreversibilities are:

• friction (resulting from flow of matter), e.g.: pipes, turbines, compressors
• heat transfer with finite temperature difference in boilers and heat exchangers as result of: convection, radiation
• spontaneous chemical reactions
• chemical reaction (combustion), e.g.: combustion chamber of a boiler, combustion chamber of gas turbines
• mixing: quantities of the same substances at different temperatures different substances at the same temperature
• Electric current flow through a resistance

Question 6

Difference between first and second law again!

Answer 6

The laws of thermodynamics describe the relationships between thermal energy, or heat, and other forms of energy, and how energy affects matter.

The First Law of Thermodynamics states that energy cannot be created or destroyed; the total quantity of energy in the universe stays the same.

The Second Law of Thermodynamics is about the quality of energy. It states that as energy is transferred or transformed, more and more of it is wasted. The Second Law also states that there is a natural tendency of any isolated system to degenerate into a more disordered state.

Question 7

Through an Energy Analysis of Thermodynamic Cycles prove that the efficiency of a cycle is always smaller than 1 : 𝜂 < 1

Answer 7

Energy balance of a cycle

Δ𝐸𝑐𝑦𝑐𝑙𝑒 = Δ𝑄𝑐𝑦𝑐𝑙𝑒 − 𝑊𝑐𝑦𝑐𝑙𝑒

Since we return to the orginial state there is no net change in the cycle energy and thus

𝑊𝑐𝑦𝑐𝑙𝑒 = Δ𝑄𝑐𝑦𝑐𝑙𝑒

This applies to every thermodynamic cycle independent of the processes

So for 𝑊𝑐𝑦𝑐𝑙𝑒 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡

we define the thermal efficiency 𝜂 = 𝑊𝑐𝑦𝑐𝑙𝑒/𝑄_𝑖𝑛 and if we fill in the above 𝜂 = (𝑄_𝑖𝑛 − 𝑄_𝑜𝑢𝑡)/ 𝑄_𝑖𝑛 = 1 − 𝑄_𝑜𝑢𝑡 /𝑄_𝑖𝑛

–>From this we see that always 𝜂 < 1

Question 8

What is the Clausius Inequality?

Answer 8

From Clausius and Kelvin-Planck we learn that we need a hot and a cold reservoir for any thermodynamic cycles.

Clausius inequality: Contour Integral of (𝛿𝑄 /𝑇) _𝑏 ≤ 0

with 𝛿𝑄 heat transfer and T absolute temperature at a given part of the system boundary b

Introducing an arbitary „entropy“ variable S we can reformulate:

(𝛿𝑄 /𝑇) _𝑏 = −𝑆

with:

• S=0: no irreversibilites
• S>0: irreversibilites present
• S<0: impossible

Question 9

Which are the properties that describe the thermal state of a system?

Answer 9

p,T,v are properties which describe the thermal state of a system

Note: There are also caloric properties which are energy-based (e.g. internal energy u, enthalpy h and entropy s)

Question 10

What happens when water transforms

• from gas state to solid state?
• and from gas to liquid?
• from gas to plasma?

Answer 10

• sublimination
• condensation
• ionization

Question 11

What is the saturation state?

Answer 11

Saturation state: A state at which a phase change occurs.

Saturated liquid and vapor are considered as two different systems at equilibrium.

Question 12

What measure describes the amount of vapor and liquid in vapor liquid mixture?

Answer 12

The so called steam quality x is an important measure to describe the amount of vapor and liquid in a vapor-liquid mixture. This is information which is not contained in the relation 𝑝_𝑠 = 𝑓(T) describing the equilibrium at saturation state.

𝑥 = 𝑚_{𝑣𝑎𝑝𝑜𝑟} /(𝑚_{𝑙𝑖𝑞𝑢𝑖𝑑} + 𝑚_{𝑣𝑎𝑝𝑜𝑟} )

= 𝑚”/ (𝑚′ + 𝑚” )= 𝑚”/𝑚

𝑥 = 0 saturated liquid 𝑥 = 1 saturated steam/vapor

Question 13

In this T-s diagram of water please name the different lines in the graph:

Answer 13

• Red: constant enthalpy „isenthalps“
• Black: constant pressure „isobars“
• Green: constant volume „isochors“
• Blue: saturation state
• Blue dashed: constant vapor quality

Question 14

Do Excercise 3

Question 15

Do excercise 4

Question 16

Do Excercise 5