Kerala Plus One Physics Notes Chapter 12 Thermodynamics
Thermodynamics is a branch of physics which deals with study of heat, temperature and the transformation of heat energy into other forms of energy and vice-versa. In thermodynamics state of system is specified by macroscopic variables such as pressure, temperature, volume, mass, composition, etc.
A group of a large number of particles having a certain value of pressure, volume and temperature is called a thermodynamic system.
- Surroundings: Everything outside the thermodynamic system is its surrounding.
- Thermodynamic variables: These are quantities like pressure (P ), volume (v), and temperature (T) which help us to study the behaviour of a thermodynamic system.
- Thermodynamic process: It is any process in which there is some change in pressure, volume or temperature of a system.
- Thermodynamic equilibrium: A system is said to be in the state of thermodynamic equilibrium if the macroscopic variables like pressure, volume, temperature, mass etc., do not change with time.
Thermodynamic State variables:
Thermodynamic state variables of a system are the parameters which describe equilibrium states of the system.
- Extensive varibales depend on size of the system, eg., mass, internal energy, volume.
- Intensive varibales are independent of size of system, eg., pressure, temperature, density. For example the equation of state of an ideal gas is given by PV – nRT ; where n is the number of moles of the gas and R is gas constant.
=-ΔW. That is work is done on the gas which increases its internal energy. Hence temperature of the gas rises.
Zeroth law of Thermodynamics:
It states that if two systems A and B are separately in thermal equilibrium with a third system C, then the systems A and B are in thermal equilibrium with each other also.
Concept of Temperature:
If two systems are said to be in thermal equilibrium it is necessary that their temperature must be same, ie., there is no flow of heat between two systems in thermal contact, when their temperature is same.
Heat, Internal energy and Work:
Internal energy of a system is sum of kinetic energies and potential energies of the molecules of the system. Thus internal energy,
U = K.E + RE
Internal energy of a system depends on the state of the system, but not how the state was achieved, ie., not on the path taken to arrive at that state.
Two ways to change the internal energy of a gas:
- Heat the cylinder containing the gas or keep the cylinder in contact with a body at higher temperature. Some heat flows from hotter body to the gas due to the temperature difference. Thus, internal energy of the gas increases.
- Push the piston down by raising some weight attached to it. Work is done on the gas. This also increases the internal energy of the gas.
Therefore heat and work are two different modes of changing the internal energy of the system. Hence heat and work in thermodynamics are not state variables, but the internal energy is a state variable.
Quasistatic process (nearly static):
It is a process in which a thermodynamic system proceeds extremely slowly such that at every instant of time, the temperature and pressure are the same in all parts of the system. In a quasistatic process, the difference in the pressure of the system and the external pressure is infinitesimally (extremely) small. Similarly the difference between the temperature of the system and temperature of the surroundings is infinitesimally small.
Isothermal process or change:
A change in pressure and volume of a gas without any change in its temperature is called an isothermal process.
In such a process, if heat is developed in the system, it is given out to the surroundings or if heat is lost, it is taken from the surroundings, so that the temperature of the system remains unchanged.
Conditions for isothermal process:
- Walls of container must be perfectly conducting to allow free exchange of heat.
- Compression or expansion should be slow as to provide time for the exchange of heat. Consider some gas contained in a barrel of conducting material, attached with a airtight piston. When the gas is compressed heat is developed. This heat goes out (is liberated) to keep the temperature constant. When the gas is made to expand, heat is spent for expansion (loss of heat). This is compensated by the transfer of heat from the surroundings (absorption) to keep the temperature constant. Such a change is called isothermal change or process. Since temperature is kept constant, Boyle’s law can be applied to study this change.Therefore the equation of state for isothermal change is given by:
P V = constant
For ideal gas in an isothermal process, there is no change in internal energy of the gas.
A gas does work during isothermal expansion. What is the source of mechanical energy so produced?
By first law of thermodynamics, ∆Q = ∆U +∆W. But for an isothermal process, ∆U=0, so ∆W = ∆Q. Thus the energy required for doing mechanical work during an isothermal process is obtained as heat by the gas from the surroudings.
An adiabatic process in one in which the pressure, volume and temperature of the system change but there is no exchange of heat between the system and surroundings.(∆Q = 0)
Conditions for adiabatic process:
- Walls of container must be perfectly non-conducting.
- Compression or expansion should be sudden, so that there is no time for the exchange of heat.
Some examples of nearly perfect adiabaic processes:
• Sudden bursting of the tube of bicycle tyre.
• Expansion of steam in cylinder of steam engine.
The temperature of a gas rises during an adiabatic compression, although no heat is given to the gas from outside. Why?
By first law of thermodynamics, ∆Q=∆U+∆ W
For an adiabatic compression, ∆Q=0, so ∆U
= – ∆W. That is work is done on the gas which increases its internal energy. Hence temperature of the gas rises.
The equation of state for adiabatic change is given by PVγ = K, a constant.
A certain gas at atmospheric pressure is compressed adiabatically so that its volume becomes half of its original volume. Calculate the resulting pressure in Nm-2. Given y for air = 1:4.
- Isobaric change: A change in volume and temperature of gas, which takes place at constant pressure is called an isobaric change.
- Isochoric change: A change in pressure and temperature, which takes place at constant volume is called isochoric change.
- Cyclic process: It is a thermodynamic process in which the system returns to its initial state after undergoing a series of changes. In a cyclic process, the P-V diagram will be a closed loop and the area of this loop gives the work done by the system.
- Non-cyclic process: It is a process in which the system does not return to x its initial state after a series of changes.
First law of Thermodynamics:
According to first law, “whenever heat is added to a system, it transforms to an equal amount of energy in some other form”.
Let an amount of heat ∆Q be supplied to a system. This heat will be used for two purposes.
- Increase the internal energy of the system, if the heat remains in the system ∆ U.
- Do external work, if it leaves the system. (∆W)
According to first law of thermodynamics,
∆Q = ∆U+∆W
Thus according to first law of thermo dynamics, the energy supplied to a system Increases partially the internal energy of the system and the rest is spent in doing work on the environment.
Also, consider the figure below:
The gas does work in moving the piston. The work done by the gas against the constant pressure P is
Δ W=Fdx = PAdx
So first law of thermodynamics also has the form,
We have seen the above formula in the last chapter and definitions of Cp and Cv. Now let’s see how this relation is derived.
According to 1st law of thermodynamics, ΔQ=ΔU+PΔV
If the heat Δ Q is absorbed at constant volume, then Δ V = 0 and we have
Here we dropped the subscript because the internal energy U of an ideal gas depends only on its temperature T.
If now the ΔQ heat is absorbed at constant pressure then,
Note: Cp is greater than Cv because when one mole of gas is heated at constant V, the heat is used only to increase the U of the gas. But when the gas is heated at constant P, the heat is used for increasing U and also for doing external W during expansion. Hence, Cp is greater than Cv
Calculate the specific heat at constant volume for a gas. Given specific heat at constant pressure is 85 cal mol-1 Hr-1, R=8.31 J mot-1 K-1 and J=4.18 J cat-1?
It is a device which converts continuously heat energy into mechanical energy for this a system is made to undergo a cyclic process. A heat consists of three parts:
- Source of heat at higher temperature Tr
- Working substance which performs mechanical work when heat is supplied to it.
- Sink, which is a heat reservoir at a lower temperature Ts.
In every cycle, the working substance absorbs an amount of heat Q1 from the source at temperature Tr It converts a part of this heat energy into mechanical work Wand releases the remaining heat Q2 to the sink at lower temperature T2.
The work done by the working system in a cycle, is transferred to the environment via some arrangement, eg., the working substance may be in a cylinder with a moving piston that transfers mechanical energy to the wheels of a vehicle through a shaft.
Here the change in heat (Q1 – Q2) is converted into work (mechanical energy)
Q1-Q2 = W
The efficiency of heat engine is given by,
As some heat is always rejected to the sink, Q2≠0. Therefore efficiency is always less than 1. ie., thermal efficiency of a heat engine is always less than 100%.
Did You Know? The maximum efficiency of a steam engine is around 15-16%. The maximum efficiency of a petrol engine is 26% and that of a diesel engine is 40%. This explains why diesel cars give more mileage than petrol cars.
Heat engine can be of two types:
- External combustion engine in which heat is produced by burning the fuel in a chamber outside the main body (ie., cylinder and piston arrangement) of the engine, eg., steam engine.
- Internal combustion engine in which the heat needed for the engine is produced by burning the fuel inside the main cylinder, eg., petrol and diesel engines.
Refrigerators and Heat pumps:
Refrigerator is reverse of heat engine, the device used to cool a portion of space (inside a chamber) is refrigerator. The device used to pump heat into a portion of space (to warm-up-room) is called heat pump.
In both devices the working substance absorbs heat Q2 from cold reservoir at
temperature T2. Some external work (by compression of gas by electric means) is done on it and heat Q1 is supplied to hot reservoir at T1
Working cycle of refrigerator:
- Sudden expansion of the gas from high pressure to low pressure results in cooling of the gas. This converts the gas into a vapour-liquid mixture at lower
- This mixture absorbs heat from the region to be cooled and gets converted into vapours.
- The vapour is heated by external work by the supply of electric power to the refrigerator.
- The heated vapours then release the heat to the surrounding and then comes to initial temperature T2.
The work done on the system is given by,
The coefficient of performance (α) of a refrigerator is defined as the ratio of quantity of heat removed per cycle from contents of the refrigerator (Q2) to the energy spent per cycle (W) to remove this heat.
(1) The water and other food stuff to be cooled in the refrigerator are the sink at lower temperature and the atmosphere or surrounding air at room temperature is the source.
(2) Although for heat engine η cannot exceed 1. But α of refrigerator can be
greater than 1.
Second Law of Thermodynamics:
The first law of thermodynamics is about conservation of energy. But this can cause
impossible situations, eg., two bodies at same temperature are in contact. One of them can cool down and the other can heat up and if total heat energy is constant the first law is not broken. But we don’t see such things happening. So, there must be another law that forbids these kind of happening. This law is the second law of thermodynamics
“ heat flows spontaneously from a substance at higher temperature to another at lower tempertaure. Heat does not flow spontaneously in the reverse direction”.The other two forms of second law of thermodynamics are:
It is impossible to construct a heat engine which would absorb heat from the reservoir and convert 100% of the heat absorbed into work.
It is impossible to design a self acting machine, which would transfer heat from a body at lower temperature to another body at a higher temperature without any external energy. This explains why our refrigerators cannot work without electric power.
Any process which can be reversed by varying its conditions such that, the reverse
process passes exactly throughout the same state as in the direct process.
Thus during the direct process, if heat is absorbed, during the reverse process, the same amount of heat is liberated (given out).
Conditions for a process to be reversible:
- The process must be quasi-static. For this, the process should be carried out
extremely slowly so that the system remains in thermal equilibrium (all parts of system and surrounding at same T) and mechanical equilibrium (no unbalanced force) with the surroundings throughout.
- Loss of heat due to friction, viscosity, resistance, etc should be completely absent.
But infact no process is perfectly reversible. Some examples which are approximately reversible are:
- Slow compression of a spring.
- An ideal gas allowed to expand slowly and then compressed slowly in a cylinder with a fricationless movable piston
It is an ideal reversible heat engine that operates between two temperatures T1 (source) and T2 (sink).
Change insulating pad to insulating stand:
- Working substance: It is an ideal gas taken in a cylinder with perfectly insulating walls and perfectly conducting base. The cylinder is fitted with a insulating and frictionless piston.
- Source: It is a body of infinite heat capacity kept at a constant high temperature T1 So any amount of heat can be drawn from it without changing its temperature.
- Sink: It is a body of infinte heat capacity, kept at a lower temperature T2 So any amount of heat can be added to it without changing its temperature.
- Insulating stand: When the base of the cylinder is attached to the insulating stand, the working substance gets isolated from the sourroundings.
1. Isothermal expansion: The cylinder is placed on the source. The gas is allowed to expand isothermally. Hence the working substance takes necessary heat from the source for expanding to keep the temperature constant. If Q1 heat is absorbed from the source and W1 work is done by the gas in isothermal expansion which takes its state from (P1 ,V1 ,T1 ) to (P2, V2, T2).
2. Adiabatic expansion: The gas is now placed on the insulating stand and allowed to expand slowly till its temperature falls to T2
If W2 work is done by the gas in the adiabatic expansion which takes its state from (P2, V2, T1) to (P3, V2, T2)
3. Isothermal compression: The gas is now placed in thermal contact with the sink at temperature T2. The gas is slowly compressed so that as heat is produced, it easily flows to the sink. The temperature of the gas remains constant at T2. If Q2 heat is released by the gas to sink and Ws work is done on the gas by the surroundings in the isothermal compression which takes its state from (P3, V2, T2) to (P4, V4, T2), then
4. Adiabatic compression: The cylinder is again placed on the insulating stand. The gas is further compressed slowly till it returns to its initial state (P1 V1 T1 )
If W3 is the work done in the adiabatic compression from (P4, V4, T2) to (P1 V1 T1).
Efficiency of heat engine:
Efficiency is the ratio of the amount of heat converted into useful work to the amount of heat absorbed from the source.
If Q1 is the heat taken from source and Q2 is, heat rejected to sink, then
We know, T1 > ( T1 – T2). Therefore, η will always less than unity or less than 100%.
5. What is the efficiency of a Carnot engine working between ice point and steam point?
Carnot showed that,
- no engine can be more efficient than the perfectly reversible engine. No heat engine working between two given temperatures can have efficiency greater than that of a reversible engine working between the same temperatures.
- The efficiency of the Carnot engine is independent of the nature of the working substance.