11th Physics Volume

A o (b) Area expansion V T V o V o (c) Volume expansion Figure . Expansion joints for safety Unit Heat and thermodynamics Solution D L L = α L ΔT ΔL = α L L ∆T ΔL = × − × × = . m= mm Area Expansion For a small change in temperature ΔT the fractional change in area ∆   A of a substance is directly proportional to ΔT and it can be written as D A A = α A ΔT Therefore, α A = D D Where, α A = coefficient of area expansion. ΔA = Change in area A = Original area ΔT = Change in temperature Volume Expansion For a small change in temperature ΔT the fractional change in volume ∆   V of a substance is directly proportional to ΔT.

D V V = α V ΔT Therefore, α V = ∆ ∆ expansion in volume is termed as volume expansion . It is shown in Figure . Linear Expansion In solids, for a small change in temperature ΔT, the fractional change in length ∆   L is directly proportional to ΔT. D L L = α L ΔT Therefore, α L = D D Where, α L = coefficient of linear expansion.

ΔL = Change in length L = Original length ΔT = Change in temperature. • When the lid of a glass bottle is tight, keep the lid near the hot water which makes it easier to open. It is because the lid has higher thermal expansion than glass. • When the hot boiled egg is dropped in cold water, the egg shell can be removed easily.

It is because of the different thermal expansions of the shell and egg. EXAMPLE . Eiffel tower is made up of iron and its height is roughly m. During winter season (January) in France the temperature is °C and in hot summer its average temperature °C.

Calculate the change in height of Eiffel tower between summer and winter. The linear thermal expansion coefficient for iron α = × − per °C Unit Heat and thermodynamics on the top surface above the liquid water (ice floats). This is due to the anomalous expansion of water. As the water in lakes and ponds freeze only at the top the species living in the lakes will be safe at the bottom.

Figure . Anomalous expansion of water in lakes °C °C Summer winter Where, α V = coefficient of volume expansion. ΔV = Change in volume V = Original volume ΔT = Change in temperature Unit of coefficient of linear, area and volumetric expansion of solids is ˚C - or K - For a given specimen, = α L ΔT (Linear expansion) ≈ α L ΔT (Area expansion ≈ × Linear expansion) ≈ α L ΔT (Volume expansion ≈ × Linear expansion) Note . .

Anomalous expansion of water Liquids expand on heating and contract on cooling at moderate temperatures. But water exhibits an anomalous behavior. It contracts on heating between ˚C and ˚C. The volume of the given amount of water decreases as it is cooled from room temperature, until it reach ˚C .

Below ˚C the volume increases and so the density decreases. This means that the water has a maximum density at ˚C . This behavior of water is called anomalous expansion of water. It is shown in the Figure .

In cold countries during the winter season, the surface of the lakes will be at lower temperature than the bottom as shown in the Figure . . Since the solid water (ice) has lower density than its liquid form, below °C, the frozen water will be y Temperatureº C x . .

. . . Density of water (g cm - ) (b) Temperatureº C x .

. . . y Volume of 1kg of water (cm ) Temperatureº C (a) Figure .

Anomalous Expansion of water Unit Heat and thermodynamics Q = m × L Therefore, L = Q Where L = Latent heat capacity of the substance Q = Amount of heat m = mass of the substance The SI unit for Latent heat capacity is J kg – . Figure . Temperature versus heat for water Melting Vaporization Solid Liquid Gas Temperature Energy When heat is added or removed during a change of state, the temperature remains constant. Note • The latent heat for a solid - liquid state change is called the latent heat of fusion (L f ) • The latent heat for a liquid - gas state change is called the latent heat of vaporization (L v ) • The latent heat for a solid - gas state change is called the latent heat of sublimation (L s ) Triple point The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid and solid) of that substance coexist in thermodynamic equilibrium.

The triple point of water is at . K and a partial vapour pressure of . Pascal. .

. Change of state All matter exists normally in three states as solids, liquids or gases. Matter can be changed from one state to another either by heating or cooling. Examples: .

Melting (solid to liquid) . Evaporation (liquid to gas) . Sublimation (solid to gas) . Freezing / Solidification (liquid to solid) .

Condensation (gas to liquid) Figure . Change of states of matter Liquid Solid Condensation Evaporation Gas Sublimation Deposition Melting Solidification Latent heat capacity: While boiling a pot of water, the temperature of the water increases until it reaches ˚C which is the boiling point of water, and then the temperature remains constant until all the water changes from liquid to gas. During this process heat is continuously added to the water. But the temperature of water does not increase above its boiling point.

This is the concept of latent heat capacity. Latent heat capacity of a substance is defined as the amount of heat energy required to change the state of a unit mass of the material. Unit Heat and thermodynamics Figure . Calorimeter with sample of block Termometer Stirrer Calorimeter cup Water Air (insulation) Insulating wood Sample Q gain = − Q lost Note the sign convention.

The heat lost is denoted by negative sign and heat gained is denoted as positive. From the definition of specific heat capacity Q gain = m s ( T f – T ) Q lost = m s ( T f – T ) Here s and s specific heat capacity of hot sample and water respectively. So we can write m s ( T f – T ) = − m s ( T f – T ) m s T f – m s T = − m s T f + m s T m s T f + m s T f = m s T + m s T The final temperature T f = m s T m s T m s m s EXAMPLE . If L of water at °C is mixed with 4L of water at °C, what will be the final temperature of water?

Take the specific heat capacity of water as J kg - K - . . . Calorimetry Calorimetry means the measurement of the amount of heat released or absorbed by thermodynamic system during the heating process.

When a body at higher temperature is brought in contact with another body at lower temperature, the heat lost by the hot body is equal to the heat gained by the cold body. No heat is allowed to escape to the surroundings. It can be mathematically expressed as Q gain = − Q lost Q gain + Q lost = Heat gained or lost is measured with a calorimeter. Usually the calorimeter is an insulated container of water as shown in Figure .

. Figure . Calorimeter Termometer Stirrer Calorimeter cup Water Air (insulation) Insulating wood A sample is heated at high temperature ( T ) and immersed into water at room temperature ( T ) in the calorimeter. After some time both sample and water reach a final equilibrium temperature T f .

Since the calorimeter is insulated, heat given by the hot sample is equal to heat gained by the water. It is shown in the Figure . Unit Heat and thermodynamics Conduction Conduction is the process of direct transfer of heat through matter due to temperature difference. When two objects are in direct contact with one another, heat will be transferred from the hotter object to the colder one.

The objects which allow heat to travel easily through them are called conductors. Thermal conductivity Thermal conductivity is the ability to conduct heat. The quantity of heat transferred through a unit length of a material in a direction normal to unit surface area due to a unit temperature difference under steady state conditions is known as thermal conductivity of a material. Figure .

Steady state heat flow by conduction. Material having thermal conductivity K Area A T > T T