Thermal Equilibrium

• Two systems are said to be in thermal equilibrium if the temperatures of the two systems are equal. 

• In mechanics if the net force on a system is zero, the system is in equilibrium.  

• In Thermodynamics equilibrium means all the macroscopic variables (pressure, temperature and volume) don’t change with time. They are constant throughout.

K= p /2m
p= square root.2mK
Decrease in Kinetic energy= 19% of K
i.e 19/100 * K = 0.19 K
Final K.E , K'= 0.81
Final momentum, p' = square rt. 2mK' = sqr. rt. 2m x 0.81K
= 0.9 square root 2mK = 0.9p
increase in p
p-p'/p x 100 = p-0.9p/p x 100 = 10%

Torque

Torque is defined as the moment of force i.e. the rotating effect produced by a given force.

It is essentially the rotational analogue of force.

Torque=force applied(f)× distance between axis of rotation and force applied(r)× sine of angle between force and distance(r)

Work:

In physics,work is said to be done when a force (F) acts on a body and the point of application of force is displaced(s) in the direction of applied force .

Workdone= applied force × displacement of the body on which force is applied

W = F• s

Bernoulli’s Principle

• For a streamline fluid flow, the sum of the pressure (P), the kinetic energy per unit volume (ρv²/2) and the potential energy per unit volume (ρgh) remain constant.
• Mathematically:- P+ ρv²/2 + ρgh = constant
  • where P= pressure ,
  • E./ Volume=1/2mv²/V = 1/2v²(m/V) = 1/2ρv²
  • E./Volume = mgh/V = (m/V)gh = ρgh

Derive: Bernoulli’s equation

Assumptions:

1. Fluid flow through a pipe of varying width.
2. Pipe is located at changing heights.
3. Fluid is incompressible.
4. Flow is laminar.
5. No energy is lost due to friction:applicable only to non-viscous fluids.

• Mathematically: -
• Consider the fluid initially lying between B and D. In an infinitesimal timeinterval Δt, this fluid would have moved.
  • Suppose v₁= speed at B and v₂= speedat D, initial distance moved by fluid from to C=v₁Δt.
  • In the same interval Δtfluid distance moved by D to E = v₂Δt.
  • P₁= Pressureat A_1, P₂=Pressure at A₂.
  • Work done on the fluid atleft end (BC) W₁ = P₁A₁(v₁Δt).
  • Work done by the fluid at the other end (DE)W₂ = P₂A₂(v₂Δt)
• Net work done on the fluid is W₁ – W₂ = (P₁A₁v₁Δt− P₂A₂v₂Δt)
• By the Equation of continuity Av=constant.
  • P₁A₁ v₁Δt - P₂A₂v₂Δt where A₁v₁Δt =P₁ΔV and A₂v₂Δt = P₂ΔV.
• Therefore Work done = (P₁− P₂) ΔVequation (a)
  • Part of this work goes in changing Kinetic energy, ΔK = (½)m (v₂² – v₁²) and part in gravitational potential energy,ΔU =mg (h₂ − h₁).
• The total change in energy ΔE= ΔK +ΔU = (½) m (v₂² – v₁²) + mg (h₂ − h₁). (i)
• Density of the fluid ρ =m/V or m=ρV

• Therefore in small interval of time Δt, small change in mass Δm
  • Δm=ρΔV (ii)
• Putting the value from equation (ii) to (i)

• ΔE = 1/2 ρΔV (v₂² – v₁²) + ρgΔV (h₂ − h₁)  equation(b)
• By using work-energy theorem: W = ΔE
  • From (a) and (b)
  • (P₁-P₂) ΔV =(1/2) ρΔV (v₂² – v₁²) + ρgΔV (h₂ − h₁)
  • P₁-P₂ = 1/2ρv₂² - 1/2ρv₁²+ρgh₂ -ρgh₁(By cancelling ΔV from both the sides).
• After rearranging we get,P₁ + (1/2) ρ v₁² + ρg h₁ = (1/2) ρ v₂² + ρg h₂
• P+(1/2) ρv²+ρg h = constant.
• This is the Bernoulli’s equation.

• A thermodynamic process is reversible if the process can be turned back such that the system and surroundings return to their original states, with no other change anywhere else in the universe.

• This means in the Reversible processes if a process starts from initial state then it goes to final state and then it can reversed back from final state to initial state.
• Examples:- Isothermal expansion and compression,  Electrolysis 

The Scientific method is a process with the help of which scientists try to investigate, verify or construct an accurate and reliable version of any natural phenomena. They are done by creating an objective framework for the purpose of scientific inquiry and analyzing the results scientifically to come to a conclusion which either supports or contradicts the observation made at the beginning.