Md. Kamrul Hasan Reza Department of Physics
Khulna University of Engineering & Technology
Khulna-9203, Bangladesh
Tel.: +880-41-769468~75 Ext. 587(O), 588 (R)
e-mail: [email protected], [email protected]
Website : www.kuet.ac.bd/phy/reza/
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Welcome to my Class (trial-II)
Physics Ph 1101
11:40 AM
July 22, 2020
COVID-19 Precautions
Don’t be afraid
Be aware of the pandemic
Use appropriate outfits if you
compelled to go out
Try to maintain proper diet
Do not forget to exercise
(at least one hour) regularly
Try to follow the guidelines of WHO and Bangladesh Government
Try to stay at home
Applications of First Law of Thermodynamics Specific Heat of a Gas (T and V Independent)
If V and T are chosen as the independent variables
U = f (V, T) ….(1)
Differentiating eq. (1)
….(2)
If an amount of heat δH is supplied to a thermodynamical
system, say an ideal gas and if the volume increases by dV at a
Constant pressure P,
Then according to the first law of thermodynamics
δH = dU + δW
Here δW = P . dV
∴ δH = dU + PdV
Substituting the value of dU from eq. (2)
….(3)
….(6)
From Joule's experiment, for an ideal gas on opening the stop-
cock, no work was done and no heat transfer took place.
So, δH = 0 = dU + 0. Therefore, dU = 0. Even though the
volume changed while the temperature is constant, there is no
change in internal energy.
References: Heat and Thermodynamics – Brij Lal & N. Subrahmanyam
and materials from internet resources
….(8)
Here CP, CV and R are expressed in the same units.
From eq. (3)
….(9)
For a process at constant temperature
dT = 0
….(10)
This equation represents the amount of heat energy supplied
to a system in an isothermal reversible process and is equal to
the sum of the work done by the system and the increase in its
internal energy.
For a reversible adiabatic process
δH = 0
Therefore from eq. (9)
Slopes of Adiabatics and Isothermals In an isothermal process
PV = Constant
Differentiating eq. (15)
P dV + V dP = 0
….(15)
….(16)
Fig. 1: P-V diagram to show the slopes of adiabats and isotherms
In an adiabatic process
P Vϒ = Constant ….(17)
Differentiating eq. (17)
P ϒ Vϒ-1 dV + V dP = 0
….(18)
Therefore, the slope of an adiabatic is ϒ times the slope of the
isothermal.
Work Done During an Isothermal Process
….(19)
Considering one gram molecule of the gas
P V = R T
Fig. 2: P-V diagram of an isotherm
….(20)
Also P1 V1 = P2 V2
….(21)
Here, the change in the internal energy of the system is zero
(temperature constant). So the heat transferred is equal to
the work done
Work Done During an Adiabatic Process
….(22)
Fig. 3: P-V diagram of an adiabat
During an adiabatic process
P Vϒ = Constant = K
Taking TA and TB as the temperatures at the points A and B
respectively and considering one gram molecule of the gas
P1V1 = R T1
and P2 V2 = R T2
Substituting these values in eq. (24)
….(24)
….(25)
Here, heat transferred is zero because the system is thermally
insulated from the surroundings. The decrease in the internal
energy of the system (due to fall in temperature) is equal to
the work done by the system and vice versa.
Relation Between Adiabatic and Isothermal Elasticities
During an isothermal process
PV = Constant
Differentiating eq.(26)
P dV + V dP = 0
….(26)
….(27)
Isothermal Elasticity
Adiabatic Elasticity
During an adiabatic process
PVϒ = Constant ….(30)
Differentiating eq. (30)
P ϒ Vϒ-1 dV + Vϒ dP = 0
….(31)
Comparing eqs. (29) and (33)
….(34)
Thus, the adiabatic elasticity of a gas is ϒ times the isothermal
elasticity
Irreversible Process
The thermodynamical state of a system can be defined with
the help of the thermodynamical coordinates of the system.
The state of a system can be changed by altering the
thermodynamical coordinates. Changing from one state to
the other by changing the thermodynamical coordinates is
called a process.
Consider two states of a system ie., state A and state B.
Change of state from A to B or vice versa is a process and the
direction of the process will depend upon a new
thermodynamical coordinate called entropy.
Consider the following processes :
Let two blocks A and B at different temperatures T1 and T2
(T1>T2) be kept in contact but the system as a whole is insulated
from the surroundings. Conduction of heat takes place between
the blocks, the temperature of A falls and the temperature of B
rises and thermodynamical equilibrium will be reached.
Consider two flasks A and B connected by a glass tube provided
with a stop cock. Let A contain air at high pressure and B is
evacuated. The system is isolated from the surroundings. If the
stop cock is opened, air rushes from A to B, the pressure in A
decreases and the volume of air increases.
processes in which the entropy of an isolated system
decreases do not take place or for all processes taking place
in an isolated system the entropy of the system should
increase or remain constant
Reversible Process
A reversible processes is one in which an infinitesimally small
change in the external conditions will result in all the changes
taking place in the direct process but exactly repeated in the
reverse order and in the opposite sense.
Second Lew of Thermodynamics
Kelvin-Planck statement of the second law is as follows:
It is impossible to get a continuous supply of work from a
body (or engine) which can transfer heat with a single heat
reservoir.
According to Kelvin, it is impossible to get a continuous
supply of work from a body, by cooling it to a temperature
lower than that of its surroundings.
According to Clausius, it is impossible to make heat flow from a
body at a lower temperature to a body at a higher temperature
without doing external work on the working substance.