- Refrigerators and heat pumps use work to move heat from a cold place to a hot place.
- Heat cannot flow from cold to hot on its own; a compressor supplies the required work.
- The refrigerant undergoes a cycle of expansion, heat absorption, compression, and heat rejection.
- The heat supplied to the hot region exceeds the heat removed from the cold region because work is added.
- A better system removes more heat from the cold region using less work.
Definitions [21]
Thermal Equilibrium Definition
Thermal equilibrium is the physical state of two bodies when they are connected by a permeable path, don’t undergo any heat transfer and both the bodies have the same temperature.
Definition: Thermometry
Thermometry is the branch of physics dealing with temperature measurement. It relies on the principle that certain physical properties of materials change continuously and predictably with temperature.
Definition: Adiabatic Wall
An adiabatic wall is an ideal partition that completely prevents heat transfer between two systems. In diagrams, it is shown as a thick, cross-hatched (slanting lines) region.
Definition: Diathermic Wall
A diathermic wall is a partition that freely allows heat to flow between two systems. It is shown as a thin dark line in diagrams. A thin copper sheet is a good example.
Definition: Thermal Equilibrium
When two bodies at different temperatures are brought into contact through a diathermic wall, heat flows from the hotter body to the cooler one. This continues until both reach the same temperature, at which point heat flow stops. This state is called thermal equilibrium.
Define heat engine.
Heat engine is a device which takes heat as input and converts this heat into work by undergoing a cyclic process.
Definition: Quasi-Static Process
Processes in which changes in the state variables of a system occur infinitesimally slowly are called quasi static systems.
Definition: Path
When a thermodynamic system changes from its initial state to its final state, it passes through a senes of intermediate states. This series of intermediate states when plotted on a p - V diagram is called a path.
Definition: lsothermal Process
A process in which change in pressure and volume takes place at a constant temperature is called an isothermal process or isothermal change.
Definition: Isobaric process
It is a constant pressure process. Boiling water at constant pressure, normally - at atmospheric pressure; is an isobaric process.
Definition: Cyclic Process
A thermodynamic process that returns a system to its initial state is a cyclic process.
Definition: Heat Engines
Heat engines are devices that transform heat partly into work or mechanical energy. Heat engines work by using cyclic processes and involve thermodynamic changes.
Definition: Refrigerators and Heat Pumps
Refrigerators and heat pumps are heat engines that work in backward direction. They convert mechanical work into heat.
Definition: Refrigerator
Refrigeration is a process of cooling a space or substance of a system and/or to maintain its temperature below its ambient temperature. In simple words, refrigeration is artificial cooling.
Definition: Kelvin–Planck Statement
It is impossible to construct a heat engine that converts all the heat absorbed from a hot reservoir completely into work.
Definition: Clausius Statement
Heat cannot flow from a colder body to a hotter body without external work being done.
Definition: Thermodynamics
Thermodynamics is the branch of physics that deals with the concepis of heat and temperature and the inter-conversion of heat and other forms of energy.
Definition: Thermal Equilibrium
When two objects are at the same temperature, they are in thermal equilibrium.
Definition: Internal Energy
Internal energy is defined as the energy associated with the random, disordered motion of the molecules of a system.
Definition: Equation of State
The mathematical relation between the state variables of a system is called the equation of state.
Definition: Thermodynamic Process
A thermodynamic process is a procedure by which the initial state of a system changes to its final state.
Formulae [12]
Conversion Formulas
Master Conversion Formula:
\[\frac{T_F-32}{180}=\frac{T_C}{100}\] = \[\frac {T_K−273.15}{100}\]
| Conversion | Formula |
|---|---|
| Celsius → Fahrenheit | TF = \[\frac{9}{5}\] × TC + 32 |
| Fahrenheit → Celsius | TC = \[\frac{5}{9}\] × (TF - 32) |
| Celsius → Kelvin | TK = TC + 273.15) |
| Kelvin → Celsius | TC = TK - 273.15) |
| Thermometric Property | T = 100 × \[\frac{(P_T-P_1)}{(P_2-P_1)}\] |
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
Formula: Isothermal Process
Q = W = nRTln\[\frac {V_f}{V_i}\]
Formula: Isobaric process
Cp = Cv + R
Formula: Isochoric Process
Q = ΔU + W = ΔU = nCv ΔT
Formula: Adiabatic Process
W = \[\frac{\left(p_{\mathrm{f}}V_{\mathrm{f}}-p_{\mathrm{i}}V_{\mathrm{i}}\right)}{\left(1-\gamma\right)}\]
Formula: Heat Engine
\[\eta=\frac{W}{Q_{\mathrm{H}}}=1+\frac{Q_{\mathrm{C}}}{Q_{\mathrm{H}}}=1-\frac{|Q_{\mathrm{C}}|}{|Q_{\mathrm{H}}|}\]
Formula: Coefficient of Performance (CoP) of a Refrigerator
K = \[\frac{\left|Q_{\mathrm{C}}\right|}{\left|W\right|}=\frac{\left|Q_{\mathrm{C}}\right|}{\left|Q_{\mathrm{C}}\right|-\left|Q_{\mathrm{H}}\right|}\]
Formula: Coefficient of Performance (CoP) of a Air Conditioner
K = \[\frac{\left|Q_{\mathrm{C}}\right|}{\left|W\right|}=\frac{Ht}{Pt}=\frac{H}{P}\]
Formula: Carnot Heat Engine
\[\eta=\frac{W}{Q_{\mathrm{H}}}=1-\frac{\left|Q_{\mathrm{C}}\right|}{\left|Q_{\mathrm{H}}\right|}=1-\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}}\]
Formula: Coefficient of Performance (CoP) of a Carnot Refrigerator
\[K=\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}-T_{\mathrm{C}}}\]
Formula: Work Done in Thermodynamic Process
W = ∫ p dV
Theorems and Laws [6]
Law: The Zeroth Law of Thermodynamics
If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.
Write the mathematical equation of the first law of thermodynamics for an isochoric process.
By substituting equation W = −pex . ΔV in the equation ΔU = q + W, we get
ΔU = q − pex . ΔV ...(1)
If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.
The equation (1) becomes ΔU = qv
Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.
State the two forms of the second law of thermodynamics.
- Kelvin–Planck statement: Heat QH cannot be taken out of a hot reservoir and used in its whole for labour W. It is necessary for QC to exhaust (give away) some of its heat to a cold reservoir. This rules out the development of an ideal heat engine.
- Clausius statement: Heat cannot transfer from a colder body to a warmer body unless some effort is made to do this. This rules out the creation of the ideal refrigerator.
Law: Zeroth Law of Thermodynamics
''If two systems are each in· thermal equilibrium with a third system; they are also in thermai equilibrium. with each other".
Law: First Law of Thermodynamics
The change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system on its surroundings.
Mathematically:
ΔU = Q − W
The first law of thermodynamics is a statement of the law of conservation of energy for thermodynamic systems. It shows that energy can neither be created nor destroyed, but can only be transformed between heat, work, and internal energy.
Law: Second Law of Thermodynamics
"The Carnot engine is the most efficient heat engine. Also, all Carnot engines operating between the same two temperatures have the same efficiency, irrespective of the nature of the working substance".
Key Points
Key Points: Thermodynamic Systems and Processes
- A thermodynamic system is the part of the universe chosen for study.
- Surroundings are everything outside the system; the boundary separates them.
- An open system exchanges both heat (energy) and matter with its surroundings.
- A closed system exchanges only heat, not matter.
- An isolated system exchanges neither heat nor matter, and a thermodynamic process changes the system's P, V, or T.
Key Points: Sign Convention for Heat
- → Heat absorbed by the system
- Q < 0 → Heat released by the system
- Q = 0 → No heat transfer (thermal equilibrium)
Key Points: Thermodynamic state variables
- A state variable is any measurable property of a system in equilibrium, like pressure, volume, or temperature.
- Intensive variables do not depend on size (pressure, temperature), whereas extensive variables do (mass, volume, internal energy).
- A system is in thermodynamic equilibrium only when all types of equilibrium exist together.
- Thermodynamic equilibrium requires uniform pressure, uniform temperature, and no chemical change in the system.
Key Points: Thermodynamic Process
- Work done by a system depends on the path taken between the initial and final states.
- The same initial and final states can be reached through different intermediate states.
- Heat transfer also depends on the path followed during the process.
- In free expansion, no heat is exchanged, and no work is done, yet the final state can be the same as in other processes.
Key Points: Reversible and Irreversible Processes
- A reversible process can be reversed completely, and the system returns to its initial state without energy loss.
- An irreversible process cannot be reversed exactly and usually involves energy loss due to friction or other dissipative forces.
- Most natural processes are irreversible, whereas theoretical thermodynamic processes are often assumed to be slow, reversible, and to involve an ideal gas.
Key Points: Refrigerators and Heat Pumps
Key Points: Limitations of First Law of Thermodynamics
- The First Law states that heat and work are interchangeable, but it does not specify which processes are physically possible.
- In practice, heat cannot completely convert into work; no heat engine can be 100% efficient.
- The Second Law imposes limits on heat flow and engine efficiency; heat cannot flow from cold to hot spontaneously.
Important Questions [11]
- What is meant by ‘thermal equilibrium’?
- What are surroundings in thermodynamics?
- Explain the change in internal energy of a thermodynamic system (the gas) by heating it.
- An ideal monoatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. What is the ratio of the final pressure to its initial pressure?
- What is mechanical equilibrium?
- In a cyclic process, if ΔU = internal energy, W = work done, Q = Heat supplied then ______.
- What is a thermodynamic process?
- Explain the cyclic process.
- Give any two types of a thermodynamic process.
- Draw a p-V diagram and explain the concept of positive and negative work. Give one example each.
- The second law of thermodynamics deals with the transfer of ______.
Concepts [12]
- Thermodynamics
- Thermal Equilibrium
- Measurement of Temperature
- Heat, Internal Energy and Work
- First Law of Thermodynamics
- Thermodynamic State Variables and Equation of State
- Thermodynamic Process
- Heat Engine
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Carnot Cycle and Carnot Engine
- Overview: Thermodynamics
