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| Measurement of Volume |
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| The space occupied by a substance is
called its volume. SI unit of volume is cubic meter (m3). The
solids whose volume can be calculated by measuring length, width, height,
diameter etc. are called regular solids. |
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| Volume of some of the regular solids can be calculated using the formulae given in the following table. |
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| 1m3 = 1m x 1m x 1m |
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| = 100 cm x 100 cm x 100 cm |
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| = 1000000 cm3 |
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| = 106cm3 |
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| Volume of irregularly shaped objects can
be found out by measuring the volume of displaced liquid by an object. We
can find the volume of these solids with the help of a measuring cylinder. |
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| (a) Measurement of volume of solids by displacement method |
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| Pour water into a clean measuring
cylinder (nearly three fourth of its volume) and note the level of water. To
avoid parallax error, reading must be taken at the lowest level of meniscus
or curved surface of the liquid as shown in the diagram below. Attach a
string to the solid and lower it into the water and note the new level of
water. The difference in the above two readings will give you the volume of
the solid. |
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| To measure the volume of an irregular body using measuring cylinder |
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| (b) Volume of an object lighter than the liquid, which will float in the liquid |
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| If the object is lighter, it will float
on water. In that case its volume can be found out with the help of a
sinker. Pour some water in a measuring cylinder and lower the sinker (any
body which sinks) into it. Note the level of water. |
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| Volume of a floating body using sinker |
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| Tie the object to the sinker and lower
them into the measuring cylinder and note the reading of water level. The
difference in water level will give you the volume of the object. |
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| (c) Volume of an irregular solid using an overflow vessel and a measuring cylinder |
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| Volume of an irregular solid can also be found by displacement method using an overflow vessel. |
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| Volume by using overflow vessel |
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| Fill the overflow vessel with water until
the water starts overflowing. When water stops overflowing place a measuring
cylinder below the overflow tube. Now gently lower the solid into the water
with the help of a string. When water stops overflowing, read the volume of
water collected in the measuring cylinder. |
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| Volume of a liquid can be measured with the help of a pipette, burette, measuring flask, or a measuring cylinder. |
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| Burette or Buret |
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| The burette is a long narrow cylinder ending with a tap and a jet at the bottom. It is graduated from the top downwards. |
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| It is calibrated in milliliters (mL) and is graduated from 0 to 50
mL. With its help exact volume can be measured. |
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| Pipette |
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| The pipette is used to transfer a fixed volume of liquid very accurately from one container to another. It consists of a long tube blown into a bulb in the middle. |
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| The lower end is drawn out into a jet, and a mark is made on the upper part of the tube to show up to what level the liquid should be drawn. To use the pipette the lower end A is dipped into the liquid and air is drawn out from the pipette for the liquid to come up. |
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| Volume of a liquid is usually measured in a unit called 'liter' |
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| 1 liter = 1000 cm3 (cc) |
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| 1 m3 = 1000 liters |
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| 1 liter = 1000 mL (milliliter) |
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| 1 mL = 1 cm3 (1 cc) |
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| Density |
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| "Which is heavier, a kg of iron or a kg of wood?" The answer is of course, "Both are equally heavy." |
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| If, however, you are asked "Which is heavier, iron or wood?" You would say, "Iron". |
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| To be precise, when we compare the heaviness of two different materials, we must refer to the same volume of each material. This leads to the concept of density. |
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| The density of a substance is defined as its mass per unit volume |
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Density  |
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| The SI unit of density is kg m-3 and in the
cgs system, the unit of density is g cm-3. |
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| The densities of different substances vary widely. Densities of most of the solids are greater than that of liquids, though there are exceptions. Densities of wood, wax and cork are less than that of water and the density of mercury is greater than most of the solids. |
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| Densities of some of the common substances are listed in the following table: |
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| The following figure shows the masses of six metals each having the same volume (unit volume 1 cm3). Aluminium is the lightest metal and gold is the heaviest. |
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| The density of aluminium is about 2.7 g cm-3 (2700 kg m-3). The density of gold is 19.3 g cm-3 (19300 kg m-3). |
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If the mass and volume of a substance can be measured, its density can be calculated using the formula  Let us take a piece of wood which has a volume of 1000 cm3 and a mass of 600 g. |
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Then its density  |
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| = 0.6 g cm-3 (600 kg m-3) |
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| A piece of aluminium of volume 100 cm3 has a much greater mass, about 270 g, than the same volume of wood. |
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Density of aluminium  |
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| = 2.7 g cm-3 (2700 kg m-3) |
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| A concrete slab 1.0 m by 0.5 m by 0.1 m
has a mass of 120 kg. What is the density of concrete slab? |
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| Volume of the concrete slab = l x b x h |
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| = 1.0 m x 0.5 m x 0.1 m |
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| = 0.05 m3 |
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| = 2400 kg m-3 |
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| An alloy is made by mixing 360 g of copper of density 9 g cm-3, with 80 g of iron of density 8 g cm-3. Find the density of the alloy, assuming the volume of each metal used does not change during melting. |
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Volume of copper  |
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| = 40 cm3 |
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Volume of iron  |
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| = 10 cm3 |
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| \ Total volume = (40 + 10) |
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| = 50 cm3 |
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| Total mass = (360 + 80) |
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| = 440 g |
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Density of alloy  |
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| = 8.8 g cm-3 |
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| Water is the most common liquid. Density of water at 4oC is 1 g cm-3 (1000 kg m-3). |
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| 28 kg of fuel completely fills a 40 liter petrol tank of a vehicle. What is the density of the fuel? (1
liter = 10-3 m3) |
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| Mass of fuel = 28 kg |
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| Volume of fuel = 40 liter |
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| = 40 x 10-3 m3 |
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| = 700 kg/m3 |
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