Physics SAE

Physics Subject Area
There are three commonly used temperature scales, Fahrenheit,
Celsius and Kelvin.
Converting Between the Kelvin and Celsius Scales
Converting Between the Fahrenheit and Celsius Scales
Thermal expansion
• Expanding solids maintain original shape
• Expanding liquids conform to the container
Linear expansion
L = length
α = coefficient of liner expansion
ΔT = temperature change
The highest tower in the world is the
steel radio mast of Warsaw Radio in
Poland, which has a height if 646m. How
much does its height increase between a
cold winter day when the temperature is
-35⁰C and a hot summer day when the
temperature is +35 ⁰C ?
= 12x10-6/ ⁰C x 646 x 70 ⁰C
= 0.54m
• Volume expansion
L = length
β = coefficient of liner expansion
ΔT = temperature change
Heat flow:
the heat current; the amount
of heat that passes by some given place on the
rod per unit time
= heat flow
k = proportionality constant, thermal conductivity
A = cross sectional area
ΔT = change in temperature
Δx = distance crossed, thickness of material
* convection
Heat is stored in a moving fluid and is carried from one place to another
by the motion of this fluid
* radiation
The heat is carried from one place to another by electromagnetic waves
* conduction
the process of handing on energy from one thing to the next
* Amount of power radiated
(I) by a body at temperature T and
having a surface area A is given by the Stefan-Boltzmann law
 =   4
I = power radiated
e = emissivity (between 0 and 1)
σ = Stefan’s constant = 5.6703 x 10-8 W/m2·K
A = surface area
T = temperature
Shiny objects are not good absorbers or radiators & have emissivity close to 0
Black objects have emissivity close to 1
Latent heat ( heat of transformation) – the heat
absorbed during the change of state

ΔQ = quantity of heat transferred
m = mass of the material
Heat of fusion - heat absorbed when changing from a
solid to a liquid
Heat of vaporization - heat absorbed when changing
from a liquid to a gas
P= pressure
V = volume
V = volume
T = temperature
P = pressure
T = temperature
Combined Gas Law
1 1
2 2
Ideal Gas Law
PV = n R T
P= pressure
V = volume
T = temperature
n = moles
R = Gas constant
= 0.08206 L-atm/mol K
*Gas Density
PV = nRT
n/V = P/RT
Molarity = n/V
Density D = m/V
Molecular Wt M = m/n
D=Mn/V =
Energy can be neither created nor
destroyed but only transformed
Energy In = Energy Out or U2 - U1 = Q -W
U1: internal energy of the system at the beginning
U2: internal energy of the system at the end
Q : net heat flow into the system
W : net work done by the system
Q = ΔU + ΔW
A closed tank has a volume of 40.0 m2 and is
filled with air at 25⁰C and 100 kPa. We want to
maintain the temperature in the tank at 25⁰C as
water is pumped into it. How much heat will have
to be removed from the air in the tank to fill it half
2  =    1
=  1 

= (100kPa) (40.0 m2)(-0.69314) = -2772.58kJ
• Isobaric
– the pressure of and on the working fluid is constant
– represented by horizontal lines on a graph
• Isothermal
– temperature is constant
– Temperature doesn’t change, internal energy remains constant, &
the heat absorbed by the gas = the work done by the gas
– The PV curve is a hyperbola
• Adiabatic
– there is no transfer of heat to or from the system
during the process
– Work done = decrease in internal energy & the temperature falls
as the gas expands
– -the PV curve is steeper than that of and isothermal expansion
Quasi-Static Processes
Quasi-static (quasi-equilibrium) processes – sufficiently
slow processes, any intermediate state can be considered
as an equilibrium state (the macroparamers are welldefined for all intermediate states).
Advantage: the state of a system that participates in a quasi-equilibrium
process can be described with the same (small) number of macro
parameters as for a system in equilibrium (e.g., for an ideal gas in quasiequilibrium processes, this could be T and P). By contrast, for nonequilibrium processes (e.g. turbulent flow of gas), we need a huge number
of macro parameters.
Examples of quasiequilibrium processes:
V = const
P = const
T = const
For quasi-equilibrium processes, P, V, T are
well-defined – the “path” between two states
is a continuous lines in the P, V, T space.
A – the
The work done by an external force on a gas
enclosed within a cylinder fitted with a piston:
W = (PA) dx = P (Adx) = - PdV
The sign: if the volume is decreased, W is positive (by
compressing gas, we increase its internal energy); if the
volume is increased, W is negative (the gas decreases
its internal energy by doing some work on the
W 1 2   
P (T , V ) dV
W = - PdV - applies to any
shape of system boundary
dU = Q – PdV
The work is not necessarily associated with the volume changes – e.g.,
in the Joule’s experiments on determining the “mechanical equivalent of
heat”, the system (water) was heated by stirring.
*Specific Heat
the heat absorbed during the change of state
Q = nCv ΔT
Q = amount of heat required
n = number of moles
Cv = specific heat at a constant volume
ΔT = Change in temperature
How to calculate changes
in thermal energy
Specific heat is the amount of heat required to raise the temperature of 1 kg of a
material by one degree (C or K).
C water = 4184 J / kg C
Q = m x T x Cp
Q = change in thermal energy
m = mass of substance
T = change in temperature (Tf – Ti)
Cp = specific heat of substance
Second Law of Thermodynamics
Entropy = the transformation of energy to a more
disordered state
- can be thought of as a measure of the randomness
of a system
- related to the various modes of motion in molecules
The second law of thermodynamics: entropy of an
isolated system not in equilibrium tends to increase
over time
• No machine is 100% efficient
• Heat cannot spontaneously pass from a colder to a
hotter object
The relationship between kinetic energy and intermolecular
forces determines whether a collection of molecules will be a
solid, liquid or a gas
* Pressure results from collisions
* The # of collisions and the KE contribute to pressure
* Temperature increase KE

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