Physical Quantities, SI Units and Unit Conversion

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Normal body temperature is thirty seven degrees Celsius, right? But a doctor using the Fahrenheit scale writes ninety eight point six, for the very same body. Same body, two different numbers! So, is there any temperature at which both thermometers show exactly the same number? Hold on to your guess; we will crack it by the end. And remember, in JEE, one wrong unit can spoil a perfect calculation. So, let's begin.

0:34The seven SI base units

So, first, the S I system. It has seven base units, and the symbol of each one is in brackets on screen. The first three you already know: length in metre, mass in kilogram, and time in second, okay? Next, electric current, in ampere, and thermodynamic temperature, in kelvin. Careful: the S I unit of temperature is the kelvin, not the degree Celsius, okay? And the last two: amount of substance, in mole, written m o l, and luminous intensity, in candela, written c d. That's it, seven. Clear?

1:11Prefixes: powers of ten

Alright, now prefixes. Instead of long strings of zeros, we put a small word before the unit. The small ones: pico is ten to the power minus twelve, nano is ten to the power minus nine, micro is ten to the power minus six, milli is ten to the power minus three, centi is ten to the power minus two, and deci is ten to the power minus one. So one millilitre is one thousandth of a litre, okay? And the big ones: kilo is ten to the power three, mega is ten to the power six, and giga is ten to the power nine. So kilo means one thousand, and mega means one million. Small prefixes below the unit, big ones above it. Easy, isn't it? Now a quick trap. Kilo means one thousand. So the real base unit of mass must be the gram, right? No, no, careful! The S I base unit of mass is the kilogram. One kilogram is ten to the power three grams, so this base unit already carries the prefix kilo. Got it?

2:13Volume and density

Now the everyday conversions. Volume first. One litre equals one cubic decimetre, which equals one thousand millilitres, which equals one thousand cubic centimetres. So one millilitre and one cubic centimetre are exactly the same volume, okay? And in the S I unit, the cubic metre: one litre is ten to the power minus three cubic metre. So one cubic metre is one thousand litres, okay? Now density, mass per volume. Since a millilitre is a cubic centimetre, one gram per cubic centimetre is the same as one gram per millilitre. On screen, centimetre to the power minus three just means per cubic centimetre, and millilitre to the power minus one means per millilitre, okay? Now think. Is one gram per millilitre the same as one kilogram per cubic metre? Not at all! It is one thousand kilogram per cubic metre. Here is why. Grams to kilograms divides the number by one thousand. But one cubic metre holds ten to the power six millilitres, so per millilitre to per cubic metre multiplies it by ten to the power six. Net effect: multiply by one thousand. That's it!

3:25Temperature: Celsius, kelvin and Fahrenheit

Next, temperature. Celsius to kelvin is easy: just add. Capital T in kelvin equals small t in degree Celsius, plus two hundred and seventy three point one five, okay? Now Celsius to Fahrenheit. We need nine by five and thirty two. So tell me, which comes first: multiply by nine by five, or add thirty two? Yes, multiply first! So, t in degree Fahrenheit equals nine by five times t in degree Celsius, plus thirty two. If you add thirty two first and then multiply, the answer comes out wrong, okay? Let's check with our hook. Thirty seven plus two seventy three point one five is three hundred and ten point one five kelvin. And nine by five times thirty seven is sixty six point six; plus thirty two, ninety eight point six. See? Same body! Just different scales.

4:24Length and pressure

Two more. For bond lengths we use the angstrom: the capital letter with a small ring on top. One angstrom is ten to the power minus ten metre, which is zero point one nanometre, or one hundred picometre, okay? And pressure. One atmosphere equals one lakh one thousand three hundred and twenty five pascal, which is one point zero one three bar, which is seven hundred and sixty millimetres of mercury, the m m H g on screen. Write these down; numericals use them all the time. With me?

4:59Topper's trick: the factor-label method

Now the topper's trick for every conversion: the factor label method. Look at this fraction: one thousand millilitres on top, one litre below. Top and bottom are the same volume, so the fraction is just equal to one. We call it a unit factor. Multiplying by one changes only the units, never the quantity. Now tell me: for litres to millilitres, should the litre sit on top of the factor, or at the bottom? At the bottom, exactly! Then the litre in your number cancels the litre below, and only millilitres are left. So multiply by as many unit factors as you need, and cancel units one by one. And the built in safety check: if the units do not cancel to the ones you want, the set-up is wrong. So stop and fix the factor before you calculate anything. Completely foolproof.

5:49Example 1: density from g/mL to kg per cubic metre

Right, example one. The density of concentrated sulphuric acid is one point eight four gram per millilitre. Express it in kilogram per cubic metre. Pause the video, and try it with unit factors. Done? Okay, let's check. Gram is on top, so the first factor has gram at the bottom: one kilogram over one thousand grams. Millilitre is at the bottom, so the next factor has millilitre on top: ten to the power six millilitres over one cubic metre. Why ten to the power six? One cubic metre is one thousand litres, and each litre is one thousand millilitres. Now cancel. Gram cancels gram, millilitre cancels millilitre, leaving kilogram per cubic metre, exactly what we wanted. One point eight four, divided by one thousand, times ten to the power six: one thousand eight hundred and forty kilogram per cubic metre. And the quick check, from our density line: one gram per millilitre is one thousand kilogram per cubic metre. So one point eight four into one thousand: one thousand eight hundred and forty. Matches, right?

7:00Example 2: when Celsius equals Fahrenheit

Now the harder one: our puzzle from the start. At what temperature do the Celsius and Fahrenheit scales show the same number? Pause and try. Hint: call that common number t. Done? Okay, let's check. If both scales show the same number, put t F equals t C equals t, in our Fahrenheit formula. So t equals nine by five t, plus thirty two, okay? Bring the t terms to one side. Now, t minus nine by five t is minus four by five t. And this arrow on screen just means 'which gives': minus four by five t equals thirty two, okay? Now, thirty two times five by four is forty. So the answer is forty degrees, right? No, no, careful! You dropped the minus sign. Classic JEE trap. So t equals thirty two times minus five by four, that is, minus forty. So minus forty degrees Celsius is exactly minus forty degrees Fahrenheit! At minus forty, both thermometers show the same number. Puzzle solved! And always check. Nine by five of minus forty is minus seventy two; plus thirty two, minus forty. Spot on, isn't it?

8:18Quick revision: SI units, volume and factor-label method

So, quick revision. Seven S I base units; mass in kilogram, temperature in kelvin. One litre is one thousand millilitres, or ten to the power minus three cubic metre, and one gram per millilitre is one thousand kilogram per cubic metre. And for every conversion, multiply by unit factors until the units cancel. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!