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Orders of Magnitude and Units. The ‘mole’: - The amount of a substance can be described using ‘moles’. ‘One mole’ of a substance has 6 x 10 23 molecules in it. (This number is called the Avogadro constant)
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The ‘mole’: • - The amount of a substance can be described using ‘moles’. • ‘One mole’ of a substance has 6 x 1023 molecules in it. (This number is called the Avogadro constant) • So a chemist may measure out 3 moles of sulphur and she would know that she has 18 x 1023 molecules of sulphur.
1.1 The Realm of Physics Q1. How many molecules are there in the Sun? Info: - Mass of Sun = 1030 kg - Assume it is 100% Hydrogen - Avogadro constant = No. of molecules in one mole of a substance = 6 x 1023 - Mass of one mole of Hydrogen = 2g A. Mass of Sun = 1030 x 1000 = 1033 g No. of moles of Hydrogen in Sun = 1033 / 2 = 5 x 1032 No. of molecules in Sun = ( 6 x 1023 ) x ( 5 x 1032 ) = 3 x 1056 molecules
Orders of Magnitude Orders of magnitude are numbers on a scale where each number is rounded to the nearest power of ten. This allows us to compare measurements, sizes etc. E.g. A giraffe is about 6m tall. So to the nearest power of ten we can say it is 10m = 1x101m = 101m tall. An ant is about 0.7mm tall. So to the nearest power of ten we can say it is 1mm = 1x10-3m = 10-3m tall. So if an ant is 10-3m tall and the giraffe 101m tall, then the giraffe is bigger by four orders of magnitude.
Q2. There are about 1x1028 molecules of air in the lab. So by how many orders of magnitude are there more molecules in the Sun than in the lab? • 1056 / 1028 = 1028 so 28 orders of magnitude more molecules in the Sun. • Q3. Determine the ratio of the diameter of a hydrogen atom to the diameter of a hydrogen nucleus to the nearest order of magnitude. • A. Ratio = 1015 / 1010 = 105
Quantities and Units A physical quantity is a measurable feature of an item or substance. A physical quantity will have a value and usually a unit. (Note: Some quantities such as ‘strain’ are dimensionless and have no unit). E.g. A current of 5.3A ; A mass of 1.5x108kg
Base quantities The SI system of units starts with seven base quantities. All other quantities are derived from these.
Derived units The seven base units were defined arbitrarily. The sizes of all other units are derived from base units. E.g. Charge in coulombs This comes from : Charge = Current x time so… coulombs = amps x seconds or… C = A x s so… C could be written in base units as As (amp seconds)
Homogeneity If the units of both side of an equation can be proved to be the same, we say it is dimensionallyhomogeneous. E.g. Velocity = Frequency x wavelength ms-1 = s-1 x m ms-1 = ms-1 homogeneous, therefore this formula is correct.
Dimensional Analysis The dimensions of a physical quantity show how it is related to base quantities. Dimensional homogeneity and a bit of guesswork can be used to prove simple equations. E.g. Experimental work suggests that the period of oscillation of a pendulum moving through small angles depends upon its length, mass and the gravitational field strength, g.
So we can write Period = k mx ly gz Where k is a dimensionless constant and x,y and z are unknown numbers. So… s = kgx my (ms-2)z s1 = kgx my+z s-2z Now equate both sides of the equation: For s 1 = -2z so z = -1/2 For kg 0 = x For m 0 = y+z so y = +1/2 So… Period = k m0 l1/2 g-1/2 Or… Period = k l g
Q. • Consider a sphere (radius, r) moving through a fluid of viscosity η at velocity v. • Experimental work suggests that the force acting upon it is related to these quantities. Use dimensional analysis to determine the formula. • (Note: the units of viscosity are Nsm-2) • You should prove… F = k ηrv • (F = 6π ηrv)
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