Thermal expansion in solids, liquids and gases - class-X

When hot liquid is poured into a thick glass tumbler,it cracks.the reason is that the glass is a poor conductor of heat.when a hot liquid is poured into a tumbler ,the inner surface of the tumbler becomes hot,while the outer surface remain at room temperature.

The true increase in the volume of liquid per unit original volume per degree rise in temperature is called the coefficient of real coefficient.

If the pendulum of a clock is made of a metal like steel or brass,its length increases in summer due to increase in Temperature ,hence time period of oscillation increases and the clock goes slow.

The true increase in the volume of liquid per unit original volume of liquid per degree rise in temperature is called coefficient of volume expansion.

The coefficient of real expansion gamma_R is given by (h1 - h2) / (h2 * delta_T). Here, (80.4 - 80) / (80 * 100) = 0.4 / 8000 = 0.00005 = 5 * 10^-5 /C.

Moment of inertia I is proportional to r^2, where r is a linear dimension. Thus, I is proportional to L^2. Differentiating, dI/I = 2 * dL/L. Since dL/L = alpha * delta_T, then dI/I = 2 * alpha * delta_T.

Real expansion is the expansion of the liquid independent of where it is contained and is a property of the liquid. Apparent expansion will depend on  the container.

A fishplate is a metal bar that is bolted to the ends of two rails to join them together in a track. Because of friction between wheel and rails temperature increases. Thus a thermal expansion on rails happens. So, if rails are joined one after another without keeping any gap between them, the rails may bend. The holes through which the fish plates are fitted to join the rails are oval in shape to give sufficient space for length of the rails to increase. 

In case of low thermal conductivity, the heat is not distributed properly. When it is heated, the temperature at its outer  surface increases more than in the inner part. This means expansion on the outer part will be more than the inner part. So a stress will be generated. If the body is cooled again, the outer surface will contract more rapidly, then the inner part. This stress will generate crack in the body.

The apparent coefficient of expansion of a liquid depends on the mass of the liquid.

In room temperature, carbon dioxide is gas, hydrogen peroxide is liquid, calcium hydroxide is solid and calcium carbonate is solid.

The rails of railway tracks are made up of steel.in summer,due to considerable rise in atmospheric temperature, the rails tend to increase in length,so they bend sideways if they are not allowed to increase in length.therefore while laying the railway tracks on wooden plank,a small gap is left between the successive lengths of rail.

When we pour hot water on a tightly closed lid, it expands due to heat gained from hot water. Due to this heat lid expands and becomes loose. This is thermal expansion of solids.

When a solid gets heat it expands and on cooling it contracts. Due to this electrical and telephone cables are strung out a little loose so that in winter, as cables contract due to cooling of atmosphere and snapping may occur, can be avoided. 

Rate of cooling is proportional to Surface Area / Volume. For a sphere, SA/V = 3/r. Since diameter of A is half of B, radius of A is half of B, so SA/V for A is twice that of B.

Metals has the capacity to expand or contract due to temperature change. Metals pipe also expand in summer and contract in winter, such changes can cause deformities, inorder to avoid this, loops are joined with the metal pipe.

$\quad T = 2\pi\sqrt{\displaystyle\frac{l}{g}}$
$\quad \displaystyle\frac{\triangle T}{T} = 2\pi\times\displaystyle\frac{1}{2}(l/g)^{-1/2}\times\triangle l/l$
$\quad (\because T + \triangle T = 2\pi\sqrt{\displaystyle\frac{l+\triangle l}{g}})$
$\quad \therefore \displaystyle\frac{\triangle T}{T} = \displaystyle\frac{1}{2}\displaystyle\frac{\triangle l}{l} = \displaystyle\frac{1}{2}\propto\triangle\theta$
$\quad = \displaystyle\frac{1}{2}\times12\times10^{-6}\times(40-20) = 12\times10^{-5}$
$\quad \triangle T = T\times12\times10^{-5} = 24\times60\times60\times10^{-5} = 10.3\space s/day$

Real expansion gamma_R = gamma_apparent + gamma_vessel. Using the given ratios and two vessels, one can derive the expression for real expansion.

Railway tracks being made out of metal ( Iron ) expand due to increase in temperature in summers.

Answer is A

The properties of thermal expansion for both steel and concrete are approximately the same as both have nearly equal coefficient of expansion . This along with excellent bendability property makes steel the best material as reinforcement in concrete structures.

Its thermal expansion is practically zero. Bricks of this type are used in the melter crown of the glass furnace as they provide good resistance to creep and good mechanical strength at the operating temperature.

Bimetals are made of two different metals having different coefficient of expansion.  

The linear expansion of coefficient of brass is more than steel .The system must be cooled which causes more contraction in brass disc and less contraction in the hole of steel plate. The disc becomes loose.

The time taken for the pendulum to complete one oscillation is called period $(T)$. $T$ increases with increase in length. We know that substances expand on heating and contract on cooling.

A metal expand on heating. If a hole is made in the metal plate, the hole will also expand due to the expansion of the material. It can be explained by considering the air in the region of hole and that air will also expand on heating. Therefore, diameter of the hole increases always.