Thermal and Statistical Physics Essay Example
 Category:Physics
 Document type:Math Problem
 Level:Masters
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 Words:715
13THERMAL AND STATISTICAL PHYSICS
Thermal and Statistical Physics
Thermal and Statistical Physics
Question 1: Efficiency of a cannot cycle
The area under the curve is as below:
_{} i
This equation gives the amount of energy transferred in the process

If the process moves towards the less entropy, then heat will be removed from the system.

If the process moves towards the great entropy, then heat will be absorbed in the system.
From the TS diagram for a reversible, the amount of work done over a cyclic process is:
_{} (ii)
Evaluating equation (ii) above:
Thus the amount of energy transferred from the hot reservoir to the cold reservoir will be:
and amount of energy transferred between the system and the cold reservoir will be:
Therefore the efficiency, _{}
_{} Is the maximum system entropy
_{} Is the minimum system entropy
_{} The amount of heat entering the system
_{} The amount of heat leaving the system
_{} The absolute temperature of the hot reservoir
_{} The absolute temperature of the cold reservoir
Question 2

For a closed system
Due to charge in temperature and volume, the internal energy charges as:
Integrating the equation above:

The change in internal energy of a closed system
Because of compression or expansion of the system, the equation becomes as below replacing the work in the system.
_{}
Taking F as a function of T and V, the heat capacity is as below:

From the law of thermodynamics, for a reversible process:
Differentiating the internal energy equation
Hence, _{}
Therefore _{}

Heat capacity with constant pressure
At constant pressure: _{}
Simplifying _{}
Therefore at constant pressure:
So _{}

For a constant temperature and volume
Change in heat capacity with constant volume is given as:
The change in internal energy of a closed system
Because of compression or expansion of the system, the equation becomes as below replacing the work in the system:
_{}
Taking F as a function of T and V, the heat capacity is as below:
Therefore _{}
Question 3: Heat transfer

Heat transferred, _{}
Where: Q it the amount of heat transferred.
M is the mass
_{} is the heat capacity of the atmosphere
_{}Is the temperature change

Work done_{}
Where: W = work done
R is the ideal gas constant
P_{1 }is the pressure at the beginning
P_{2} is the final pressure
T it is the temperature
_{}
_{} 19703.72 J energy is lost in the system

Change in internal energy
Therefore _{}
Question 4

The change in internal energy of a closed system
Because of compression or expansion of the system, the equation becomes as below replacing the work in the system:
_{}
Therefore at constant volume and entropy

At constant entropy
Taking entropy at constant volume and temperature:
This becomes, _{}

At constant entropy and pressure
Therefore diving the _{} and _{} at constant pressure and entropy
Therefore _{}
But _{}
And _{}
Therefore, _{}
So, _{}
Question 5

Phase diagram of a fluid

Phase transitions

Two properties of the system that change
During the phase transition, the properties that change are pressure and volume.
The two properties that remain constant are temperature and mass.

Clapeyron’s Equation
The slope of the curve follows:
During the phase change, the temperature is constant: _{}
From the Maxwell’s relation:
Taking an integral from one phase to another:
For a closed system and using the first law of thermodynamics:
Using the fact that temperature and pressure are constant, we get:
Therefore, _{}
Substituting in the equation of pressure change:
Therefore, the equation becomes:

Clapeyron’s equation of sublimation
From the equation, _{}
Integrating the equation, _{}
Therefore for a liquid vapor boundary:
Given pressure and temperature are constant, therefore:
Question 6

Given the vapor pressure for liquid and solid and solving the equations simultaneously:
_{} i
_{} ii
Solving (i) and (ii) simultaneously
_{}

Latent heat for triple points
At the triple points _{}
Latent heat _{}
Question 7

Maximum inversion temperature of Helium
From the equation _{}
Maximum inversion temperature is at _{}
For _{}
_{} 0 = _{}
Solving the quadratic equation
_{}
Therefore, the maximum inversion temperature of Helium is _{}

Maximum inversion pressure is at maximum inversion temperature.
At 24 K, the inversion curve is at maximum therefore,
_{}
References
Balmer, R. T. (2010). Modern engineering thermodynamics. New York: Elsivier.
Clausius, R. (1879). The mechanical theory of heat.London: Macmillan & Co.
Kittel, C. (1986). Introduction to solid state physics (6th edition). New York: John Wiley.
Stanley, H. E. (1971). Introduction to phase transitions and critical phenomena. New York:
Oxford University Press.