Class 11th Physics - Thermal Properties of Matter Case Study Questions and Answers 2022 - 2023
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Thermal Properties of Matter Case Study Questions With Answer Key
11th Standard CBSE
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Reg.No. :
Physics
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Heat is a form of energy which produces the sensation of warmth. It is total thermal energy of the body which is sum of kinetic energies of all the individual molecules of the body. It is transferred from one body to the other on account of temperature difference between two bodies. Joule found that when' mechanical work (W) is converted into heat (Q), then the ratio of Wand Q is always constant, represented by J i.e., Joule's mechanical equivalent of heat.
\(J=\frac{W}{Q} \text { or } W=J Q\)
A measure of temperature is obtained using a thermometer that use Physical Properties which change uniformly with temperature, for example, in common liquid in glass thermometers, mercury, alcohol etc are used whose volume varies linearly with temperature over a wide range.
(i) Define temperature and its significance.
(ii) Define One calorie.
(iii) How does a thermometer work?
(iv) Name the two convenient fixed reference point for measuring temperature.
(v) How celsius temperature and Fahrenheit scale are related to each other?
(vi) What is absolute zero temperature?
(vii) What is Kelvin scale? How it is related with celsius scale?(a) -
When solid is heated, the amplitude of vibration of atoms and molecules increases. Therefore effective interatomic separation increases and cause thermal expansion. Thermal expansion of solids are of three types:
(i) Linear expansion
(ii) Area expansion
(iii) Volume expansion. Thermal expansion of liquid are of two kinds. Real expansion and apparent expansion that occurs in form of volume expansion. Thermal expansion of water is anomalous i.e., volume of given amount of water first decreases with increase in temperature from 0 °C to 4 °C and beyond 4 °C volume of water increases with rise of temperature. In thermal expansion of gases is more than solid and liquid but coefficient of volume expansion is dependent on temperature for gases.
(i) On what factors does the coefficient of thermal expansion depend? Write its S.I. unit.
(ii) Write the relation between the three coefficients of expansion \(\alpha, \beta\) and \(\gamma\) for solid.
(iii) A body at higher temperature contains more heat. Comment.
(iv) Why are clock pendulums usually made of invar?
(v) Draw graphical variation of volume and temperature for water.
(vi) How is coefficient of thermal expansion of gases related to temperature?
(vii) State water equivalent.(a) -
States of matter viz: solid, liquid and gas are function of temperature and heat content. During the change of state of a substance, the exchange of heat takes place between the substance and surrounding. In this process temperature of substance remains constant. At certain temperature known as melting point. Both the solid and liquid states of the substance coexist in thermal equilibrium. Similarly, at boiling point both the liquid and vapour states of the substance co-exist in the thermal equilibrium. There are certain substance which on heating directly pass from solid to vapour state without passing through the liquid state. This is sublimation process in which solid changes to vapour state of the substance. Process of change of state depends on pressure and temperature.
(i) Define triple point.
(ii) Define latent heat of a substance.
(iii) What is principle of calorimetry?
(iv) What is effect of pressure on the melting point of a substance?
(v) State phenomenon of relegation.
(vi) What is boiling point? What is effect of pressure on the boiling point?
(vii) What is sublimation?(a) -
Three cylindrical rods A, Band C of equal lengths and equal diameters are joined in series as shown in the figure. Their thermal conductivities are 2K, K and 0.5 K respectively.
100°C \(\begin{array}{|l|l|l|} \hline \mathrm{A} & \mathrm{B} & \mathrm{C} \\ \hline \end{array}\) 0°C
In the steady-state, the free ends of rods A and C are at 100 °C and a 0°C respectively. Neglecting loss of heat from the curved surfaces of rods.
(i) Determine the temperature of the junction between rods A and B.
(ii) Determine the temperature of the junction between rods Band C.
(iii) Determine the equivalent thermal conductivity of the combination.
(iv) Define coefficient of thermal conductivity of a solid. Write its S.I unit.
Two rods A and B are of equal length. Each rod has the ends at temperature T1 and T2 What is the condition that will ensure equal rates of flow of heat through the rods A and B?(a) -
All bodies emit heat energy from their surface by virtue of their temperature. This heat energy is called radiant energy or thermal radiation. The heat that we receive from the sun is transferred to us by a process which, unlike conduction and convection, does not require the help of a medium in intervening space which is almost free of particles. Radiant energy travels in space as electromagnetic waves in the infra-red region of electromagnetic spectrum. They exhibit the phenomenon of interference, diffraction, and polarization as light does.
The emission of radiation from a hot body is expressed in terms of that emitted from a reference body (called the black body) at the same temperature. A black body absorbs and emits radiations of all wavelengths. The total energy E emitted by a unit area of a black body per second is given by E = \(\sigma T^{4}\)
Where T - is absolute temperature of the body and a is Stefan's constant, if the body is not the perfect black body, then E = \(\varepsilon \sigma T^{4}\) , where \(\varepsilon\) is the emissivity of the body.
(i) Determine the dimensions of Stefan's constant a from Stefan - Boltzman law.
(ii) What is S.I unit of Stefan's constant?
(iii) In which region of the electromagnetic spectrum do thermal radiation lie?
(iv) Which device is used to detect thermal radiation?
(v) When a body A at a higher temperature T1 is surrounded by another body B at a lower temperature T2. Write the relation between the rate of loss of heat from body A and temperature.
(vi) On what factor does the rate at which energy is radiated by a body depends?
(vii) On which parameter does the colour of a star depends upon?(a)
Case Study
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Answers
Thermal Properties of Matter Case Study Questions With Answer Key Answer Keys
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(i) Temperature of a body is the measure of degree of hotness or coldness. It determines the direction of flow of heat when this body is placed in contact with another body i.e., hotter end to colder end.
(ii) One calorie is the amount of heat required at a pressure of I atm. to raise the temperature of 1 gram of water through 1oC. 1 calorie = 4.186 Joules.
(iii) Thermometer is based on change in property of matter with temperature. Some common properties are:
(i) variation of volume of liquid with temperature.
(ii) variation of pressure with temperature.
(iii) variation of resistance of metal with temperature.
(iv) variation of thermo emf with temperature of a junction in a thermocouple etc.
(iv) Reference point for measuring temperature are steam point and ice point of water at standard pressure.
(v) \(\frac{T_{C}}{100}=\frac{T_{F}-32}{180}\)
(vi) It is the temperature at which pressure P of gas would reduce to zero so also volume V of the gas. It is the lowest attainable temperature. 0 °K = -273.15 °C.
(vii) Scale of temperature with its zero at -273.15 °C and size of each degree same as on the celsius scale, is called kelvin scale
TK = t °C + 273.15 -
(i) Coefficient of thermal expansion depends on the nature of material of the solid. Its S.I unit is K-1.
(ii) Coefficient linear expansion \((\alpha)\), area expansion \((\beta)\) and volume expansion \((\gamma)\) are related as \(\alpha=\frac{\beta}{2}=\frac{\gamma}{3}\) , for solid.
(iii) Statement may not be true always because heat content of a body depends on mass of body, its specific heat and temperature.
(iv) The clock pendulums are usually made of invar because it has very low value of coefficient of linear expansion. This enables the clock to keep correct time in different seasons.
(v) Water shows the anomalous behaviour of thermal expansion.
(vi) Coefficient of volume expansion y of gas is inversely proportional to temperature T.
i.e., \(\gamma=\frac{1}{T}=\frac{\Delta V}{V \Delta T}\)
(vii) Mass of water which would absorb or evolve the same amount of heat as is done by the body in rising or falling through the same range of temperature. It is equal to product of mass of body and specific heat of body W = Sm. -
(i) It is a particular point on the P- T phase diagram representing a particular pressure and temperature at which the substance can co-exist in all the three states viz. Solid, liquid and vapour.
(ii) It is the amount of heat energy required to change the state of unit mass of a substance from solid to liquid or from liquid to vapour without any change in temperature.
(iii) Calorimeter works on the principle that heat lost by one body is equal to heat gained by other provided no heat escape from system to surrounding in any form.
(iv) Melting point of a substance decreases with increase in pressure.
(v) Phenomenon of refreezing of ice when pressure is reduced is known as relegation.
(vi) The temperature at which the liquid and vapour states of substance are in thermal equilibrium with each other i.e., vapour pressure becomes equal to external pressure. Boiling point of a substance increases with increase in external pressure.
(vii) On heating a substance, the change from solid state to vapour state without passing through the liquid state is called sublimation. e.g., camphor, iodine and solid carbon dioxide are sublime substance. -
(i) In the steady-state, the rate of flow of heat is the same for all rods.
If T1 and T2 are the temperatures at the junction points between A, Band C respectively. Then
\(\frac{Q}{t}=\frac{K_{A} A\left(100-T_{1}\right)}{d}\)
= \(\frac{K_{B} A\left(T_{1}-T_{2}\right)}{d}\)
= \(\frac{K_{C} A\left(T_{2}-0\right)}{d}\)
Given KA=2K1 KB = K and Kc =0.5K. Hence 2(100 - T1 ) = (T1 - T2 ) = 0.5(T2 - 0)
and T1 - T2 = 0.5T2
T1 = 85.7 °C.
(ii) Since T1 = 85.7 °C, therefore T2 = 57.1 °C using 200 - 2T1 = 0.5T2
(iii) Since the rods have the same lengths and the same diameters, the equivalent thermal conductivity of the series combination is
\(\frac{1}{K_{e}}=\frac{1}{K_{A}}+\frac{1}{K_{B}}+\frac{1}{K_{C}}\)
= \(\frac{1}{2 K}+\frac{1}{K}+\frac{1}{0.5 K}\)
Ke = \(\frac{2 K}{7}\)
(iv) Coefficient of thermal conductivity of a solid is equal to the rate of flow of heat per unit area per unit temperature gradient across the solid.
S.I unit of (Coefficient of thermal conductivity) K is Wm-1K-1.
(v) As \(\frac{\Delta Q_{1}}{\Delta t}=\frac{\Delta Q_{2}}{\Delta t}\)
\(\therefore \quad K_{1} A_{1} \frac{\left(T_{1}-T_{2}\right)}{L_{1}}=K_{2} A_{2} \frac{\left(T_{1}-T_{2}\right)}{L_{2}}\)
\(\Rightarrow \quad \frac{A_{1}}{A_{2}}=\frac{K_{2}}{K_{1}}\)
i.e., the cross-sectional area of two rods must be in inverse ratio of their thermal conductivities. -
(i) Stefan - Boltzman law states that E = \(\sigma T^{4}\) where E - stands for the total energy emitted per unit area per second.
Thus dimensions of E = dimensions of \(\left(\frac{\text { Energy }}{\text { area } \times \text { time }}\right)\)
i.e., \(\frac{\mathrm{ML}^{2} \mathrm{~T}^{-2}}{\mathrm{~L}^{2} \mathrm{~T}}=\mathrm{MT}\) ,therefore, dimension of
\(\sigma=\frac{\mathrm{MT}^{-3}}{\mathrm{~K}^{4}}=\mathrm{MT}^{-3} \mathrm{~K}^{-4}\)
(ii) S.I unit of Stefan's constant is Wm-2 K-4
(iii) Thermal radiations lie in the infrared region of electro magnetic spectrum.
(iv) Thermopile is used to detect thermal radiation.
(v) \(E \propto\left(T_{1}^{4}-T_{2}^{4}\right)\)
(vi) The rate at which energy is radiated by a body depends upon.
(i) the surface area of the body
(ii) the temperature of the body
(iii) nature of the surface of the body
(iv) the emissivity of the surface of the body.
(vii) According to Wein's law \(\lambda_{\mathrm{m}} \mathrm{T}\) = Constant. Colour of star depends upon its surface temperature.
Case Study