Quick Recap of Thermodynamics

Notes for Examination


Temperature

Relation between Celsius and fahrenhite scale is

TF=9/5 TC + 32°

TF - Fahrenhite Temperature
TC - Celsius Temperature

Relation between Celsius and kelvin scale is
TC = TK - 273.15 K


TK - Temperature in Kelvin
TC - Temperature in celsius


- If R0 & R100 are resistance of metak wire at ice and steam point resp then temp t can be defined corresponding to resistance RT as follows



T = (RT-R0)*100
R100-R0





- The pressure,volume and temperature in kelvin of such gases obey the equation
PV=nRT ----(1)



Thermal expansion

ΔL=αLΔT


Specific Heat Capacity



c = `Q
nΔT


Gas Laws
Boyles Law: PV=constant
Charles Law : V/T=constant
Dalton Law of Partial Pressure: P=P1 + P2 +P3
Root mean Square Velocity
Vrms=√3RT/M
Mean Square Velocity
Vm=√8RT/&#960M
Average Velocity
V=√2RT/M
Also
Vrms > Vm > V

Average kinetic Energy of Gas=3/2nRT


First law of Thermodynamics

ΔU=Q-W


Gas Processes

Isothermal Process : PV=constant ,ΔU=0,Q=W,Molar Specific Heat=infinity
Adaibatic Process : PVy=constant,Q=0,ΔU=-W,Molar Specific Heat=zero
Polytropic Process : PVn=constant,Molar Specific Heat=R/y-1 + R/1-n
Volume Constant : P/T=constant W=0,ΔU=Q,Molar Specific Heat=Cv
Pressure Constant : V/T=constant ΔU=Q-W ,Molar Specific Heat=CP

Internal energy depends on Temperature.
So for same temperature change ΔT
nCvΔT=Q1-W1=Q2-W2=Q3-W3

Molar Specfic Heat Capacity of any process is given by

C=Cv + Pdv/ndT where n is no of moles of the gas

Workdone by Gas= ∫PdV



Heat Conduction

Q=-KAdT/dx

Wein displacement lawλT4=Constant

Stefan's Law
Q=eσT4

Newton law of Cooling

dT/dx=b(T-Ts)










T =

(RT-R0)*100

R100-R0
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Some study tips for Thermodynamics

1. Always make sure you Heat(Q) ,Internal Energy(U) & Work(W) with correct sign in equation
ΔU=Q-W

W is positive when work done by the system(Increase in Volume)
W is negative when work done on the system(Decrease in Volume)
Q is positive when heat is given to the system
Q is negative when heat is taken from the system

2. workdone in a cycle is equal to the area enclosed on the PV diagram

3. Change in Internal energy is zero for a cycle
So Net Heat=Net Work done

4.All Bodies emit radiation at all temperature.Radiation emmited are of diffrent frequencies.Frequency at which most radiation are emmitted are directly proportional to Temperature of the body.

Questions for Thermodynamics

Question 1:A monoatomic gas of n moles is contained in a vertical, frictionless piston cylinder device at Temperature T. The piston has a mass of M kg with a cross-sectional area of A cm2 and the atmospheric pressure is P N/m2.
a,Determine the pressure inside.
b. what amount is heat required to double the temperature

Question 2:The pressure of the gas in constant volume gas thermometer are 80 cm,90cm and 100cm of mercury at the ice point,the steam point and in a heated wax bath resp.Find the temperature of the wax bath

Question 3.The heat capacity of a substance is found to be varies as temperature
C=C0(1+aT).
A sample of mass m of that substance is heated from tempertaure T1 to T2.How much heat is required

Question 4.A monotonic gas is taken through ABCDA cycle.
A->B Constant Pressure process
B->C Constant volume process
C->D Constant Pressure process
D->A Constant volume process

The PV coordinates of point A are (P,V)
The PV coordinates of point B are (P,3V)
The PV coordinates of point C are (3P,3V)
The PV coordinates of point D are (3P,V)

1 Find the total workdone in the cycle
2 Change in Internal energy

Question 5.The coefficent of linear expansion of a substance is found to be varies as temperature
α=α0(1+aT).
A rod of lenght L made of that substance is at tempertaure T1 .It is heated to temperature T2.What is the final length of rod

Solutions


Please take a look at other Thermal Post also
Thermal Expansion
Study Tips Part 1
Study Tips Part 2
Thermo Quick Recap
Conceptual Questions Part 1
Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
IITJEE Objective Questions part 1
IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions

Biography of Albert Einstein

The German-born American physicist Albert Einstein (1879-1955) revolutionized the science of physics. He is best known for his theory of relativity.

-Born on on March 14, 1879, in Ulm
-Early Education in Munich
-He was unable to speak fluently at age 9
-Einstein mastered differential and integral calculus by age 16
-He passed his diploma examination at the FIT in 1900
-In 1902 he was engaged as a technical expert, third-class, in the patent office in Bern, Switzerland.
-He married Mileva Maric, a former classmate in Zurich. They had two sons.
-It was in Bern, too, that Einstein, at 26, completed the requirements for his doctoral degree and wrote the first of his revolutionary scientific papers.
-In 1913 the well-known scientists Max Planck and Walter Nernst traveled to Zurich to persuade Einstein to accept a lucrative research professorship at the University of Berlin, as well as full membership in the Prussian Academy of Science. He accepted their offer in 1914
-Einstein played a key role (1939) in mobilizing the resources necessary to construct the atomic bomb by signing a famous letter to President Franklin D. Roosevelt which had been drafted by Leo Szilard and E.P. Wigner. When Einstein's famous equation E =mc2 was finally demonstrated in the most awesome and terrifying way by using the bomb to destroy Hiroshima in 1945, Einstein, the pacifist and humanitarian, was deeply shocked and distressed; for a long time he could only utter "Horrible, horrible."
-On April 18, 1955, Einstein died in Princeton.


Contributions to physics

-it began in 1905 with three major results
1.The explanation of Brownian motion in terms of molecules
2.The explanation of the photoelectric effect in terms of the quantum
3.The special theory of relativity that links time to space and energy to matter.

From 1907 to 1915 Einstein developed general relativity, a theory of gravity more accurate than Newton's; it became the basis of theoretical cosmology. In failed efforts in the 1930s to refute the interpretation of quantum theory in terms of probability, Einstein contributed to the theoretical basis for what is sometimes called teleportation of photons (which Einstein called "spooky action at a distance"). His last major effort was an attempt to unify electromagnetism and gravity into a single unified field theory, still an active problem of physics.

Quotes:

"Perfection of means and confusion of goals seem -- in my opinion -- to characterize our age."

"One must not attempt to justify them, but rather to sense their nature simply and clearly."

"In the middle of difficulty lies opportunity."

"And the high destiny of the individual is to serve rather than to rule, or to impose himself in any other way."

"It should be possible to explain the laws of physics to a barmaid."

"Education is the progressive realization of our ignorance."

Problem on Thermal Expansion

Question
A circular hole of diameter 2.00 cm is made in an aluminium plate at 0 ° C .what will be the diameter at 100° C?
α for aluminium = 2.3 * 10-3 / ° C

Solution
Thermal Expansion
- Increase in dimension of body due to increase in temperature is call thermal expansion
- Most of the solid material expand when heated

-Consider a rod of length L then for small change in temperature ΔT,the fractional change in length ΔL/L is directly propertional to ΔT
ΔL/L=αΔT --(2)
or ΔL=αLΔT --(3)
- constant α characterizes the thermal expansion properties of a particulaqr material and it is known as coefficient of linear expansion.
- for materials having no prefential direction,every linear dimension changes according to equation (3) and L could equally well represent the thickness of the rod,side lenght of the square sheet etc
-Normally metals expand more and have high value of α
- Agian consider the intial surface area A of any surface .Now when the temperature of the body is increases by ΔT ,the increase in surface area is given by
ΔA=αAAΔT ----(4)
where αA is the coefficient of area expansion
-Similary we can define coefficient of volume expansion as fractional change in volume ΔV/V of a substance for a temperature change ΔT

as ΔV=αVVΔT ----(5)
- K-1 is the unit of these coefficents expansions
- These three coefficent are not strictly constant for a substance and these value is depends on temperature range in which they are measured.

Relation between volume and linear coefficient of expansion for solid materail: Consider a solid parallopide with dimension L1,L2 and L3
then volume is
V= L1L2L3
when temperature increase by a amount ΔT then each linear dimension changes and then new volume is
V+ΔV=L1L2L3(1+αL )
V+ΔV=V(1+αLΔT)3
V+ΔV=V(1+3αLΔT+3αL2ΔT2L3ΔT3)
if ΔT is small the higher order can be neglected.Thus we find
V+ΔV=V(1+3αLΔT)
ΔV=3αLVΔT
Comparing this with equation (5) we find
αV=3αL

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