Physics · Textbook solutions

Thermal Properties of Matter

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 58 questions

7. Thermal Properties of Matter — worked examples

20 q

Solved Examples

Worked · 20
  1. Solved Ex.7.1
    Average room temperature on a normal day is 27 ∘^\circC. What is the room temperature in ∘^\circF?
  2. Solved Ex.7.2
    Normal human body temperature in feherenheit is 98.4 ∘^\circF. What is the body temperature in ∘^\circC?
  3. Solved Ex.7.3
    The length of a mercury column in a mercury-in-glass thermometer is 25 mm at the ice point and 180 mm at the steam point. What is the temperature when the length is 60 mm?
  4. Solved Ex.7.4
    A resistance thermometer has resistance 95.2 Ω\Omega at the ice point and 138.6 Ω\Omega at the steam point. What resistance would be obtained if the actual temperature is 27 ∘^\circC?
  5. Solved Ex.7.5
    Express T=24.57T = 24.57 K in celsius and fahrenheit.
  6. Solved Ex.7.6
    Calculate the temperature which has the same value on fahernheit scale and kelvin scale.
  7. Solved Ex.7.7
    The pressure reading in a thermometer at steam point is 1.367×1031.367 \times 10^{3} Pa. What is pressure reading at triple point knowing the linear relationship between temperature and pressure?
  8. Solved Ex.7.8
    The length of a metal rod at 27 ∘^\circC is 4 cm. The length increases to 4.02 cm when the metal rod is heated upto 387 ∘^\circC. Determine the coefficient of linear expansion of the metal rod.
  9. Solved Ex.7.9
    Length of an iron rod at temperature 27 ∘^\circC is 4.256 m. Find the temperature at which the length of the same rod increases to 4.268 m. (α\alpha for iron =1.2×10−5= 1.2 \times 10^{-5} K−1^{-1})
  10. Solved Ex.7.10
    A thin aluminium plate has an area 286 cm2^{2} at 20 ∘^\circC. Find its area when it is heated to 180 ∘^\circC. (β\beta for aluminium =4.9×10−5= 4.9 \times 10^{-5} /∘^\circC)
  11. Solved Ex.7.11
    A liquid at 0 ∘^\circC is poured in a glass beaker of volume 600 cm3^{3} to fill it completely. The beaker is then heated to 90 ∘^\circC. How much liquid will overflow? (γliquid=1.75×10−4\gamma_{\text{liquid}} = 1.75 \times 10^{-4} /∘^\circC, γglass=2.75×10−5\gamma_{\text{glass}} = 2.75 \times 10^{-5} /∘^\circC)
  12. Solved Ex.7.12
    A sheet of brass is 50 cm long and 8 cm broad at 0 ∘^\circC. If the surface area at 100 ∘^\circC is 401.57 cm2^{2}, find the coefficient of linear expansion of brass.
  13. Solved Ex.7.13
    If the temperature of 4 kg mass of a material of specific heat capacity 300 J/kg ∘^\circC rises from 20 ∘^\circC to 30 ∘^\circC. Find the heat received.
  14. Solved Ex.7.14
    Find thermal capacity for a copper block of mass 0.2 kg, if specific heat capacity of copper is 290 J/kg ∘^\circC.
  15. Solved Ex.7.15
    A sphere of aluminium of 0.06 kg is placed for sufficient time in a vessel containing boiling water so that the sphere is at 100 ∘^\circC. It is then immediately transferred to 0.12 kg copper calorimeter containing 0.30 kg of water at 25 ∘^\circC. The temperature of water rises and attains a steady state at 28 ∘^\circC. Calculate the specific heat capacity of aluminium. (Specific heat capacity of water, sw=4.18×103s_{w} = 4.18 \times 10^{3} J kg−1^{-1} K−1^{-1}, specific heat capacity of copper sCu=0.387×103s_{Cu} = 0.387 \times 10^{3} J kg−1^{-1} K−1^{-1})
  16. Solved Ex.7.16
    When 0.1 kg of ice at 0 ∘^\circC is mixed with 0.32 kg of water at 35 ∘^\circC in a container. The resulting temperature of the mixture is 7.8 ∘^\circC. Calculate the heat of fusion of ice (swater=4186s_{water} = 4186 J kg−1^{-1} K−1^{-1}).
  17. Solved Ex.7.17
    What is the rate of energy loss in watt per square metre through a glass window 5 mm thick if outside temperature is −20 ∘-20\ ^\circC and inside temperature is 25 ∘^\circC? (kglass=1k_{\text{glass}} = 1 W/m K)
  18. Solved Ex.7.18
    The temperature difference between two sides of an iron plate, 2 cm thick, is 10 ∘^\circC. Heat is transmitted through the plate at the rate of 600 kcal per minute per square metre at steady state. Find the thermal conductivity of iron.
  19. Solved Ex.7.19
    Calculate the rate of loss of heat through a glass window of area 1000 cm2^{2} and thickness of 4 mm, when temperature inside is 27 ∘^\circC and outside is −5 ∘-5\ ^\circC. Coefficient of thermal conductivity of glass is 0.022 cal/ s cm ∘^\circC.
  20. Solved Ex.7.20
    A metal sphere cools at the rate of 1.6 ∘^\circC/min when its temperature is 70 ∘^\circC. At what rate will it cool when its temperature is 40 ∘^\circC. The temperature of surroundings is 30 ∘^\circC.

Exercises

38 q

Choose the correct option

Practice · 6
  1. Choose the correct option.
    Ex Q.1 (i)
    Range of temperature in a clinical thermometer, which measures the temperature of human body, is
    1. A.
      70 ∘^\circC to 100 ∘^\circC
    2. B.
      34 ∘^\circC to 42 ∘^\circC
    3. C.
      0 ∘^\circF to 100 ∘^\circF
    4. D.
      34 ∘^\circF to 80 ∘^\circF
  2. Ex Q.1 (ii)
    A glass bottle completely filled with water is kept in the freezer. Why does it crack?
    1. A.
      Bottle gets contracted
    2. B.
      Bottle is expanded
    3. C.
      Water expands on freezing
    4. D.
      Water contracts on freezing
  3. Ex Q.1 (iii)
    If two temperatures differ by 25 ∘^\circC on Celsius scale, the difference in temperature on Fahrenheit scale is
    1. A.
      65∘65^\circ
    2. B.
      45∘45^\circ
    3. C.
      38∘38^\circ
    4. D.
      25∘25^\circ
  4. Ex Q.1 (iv)
    If α\alpha, β\beta and γ\gamma are coefficients of linear, area ll and volume expansion of a solid then
    1. A.
      α:β:γ\alpha : \beta : \gamma 1:3:2
    2. B.
      α:β:γ\alpha : \beta : \gamma 1:2:3
    3. C.
      α:β:γ\alpha : \beta : \gamma 2:3:1
    4. D.
      α:β:γ\alpha : \beta : \gamma 3:1:2
  5. Ex Q.1 (v)
    Consider the following statements- (I) The coefficient of linear expansion has dimension K−1^{-1} (II) The coefficient of volume expansion has dimension K−1^{-1}
    1. A.
      I and II are both correct
    2. B.
      I is correct but II is wrong
    3. C.
      II is correct but I is wrong
    4. D.
      I and II are both wrong
  6. Ex Q.1 (vi)
    Water falls from a height of 200 m. What is the difference in temperature between the water at the top and bottom of a water fall given that specific heat of water is 4200 J kg−1^{-1} ∘^\circC−1^{-1}?
    1. A.
      0.96 ∘0.96\ ^\circC
    2. B.
      1.02 ∘1.02\ ^\circC
    3. C.
      0.46 ∘0.46\ ^\circC
    4. D.
      1.16 ∘1.16\ ^\circC

Answer the following questions

Practice · 17
  1. Answer the following questions.
    Ex Q.2 (i)
    Clearly state the difference between heat and temperature?
  2. Ex Q.2 (ii)
    How a thermometer is calibrated ?
  3. Ex Q.2 (iii)
    What are different scales of temperature? What is the relation between them?
  4. Ex Q.2 (iv)
    What is absolute zero?
  5. Ex Q.2 (v)
    Derive the relation between three coefficients of thermal expansion.
  6. Ex Q.2 (vi)
    State applications of thermal expansion.
  7. Ex Q.2 (vii)
    Why do we generally consider two specific heats for a gas?
  8. Ex Q.2 (viii)
    Are freezing point and melting point same with respect to change of state ? Comment.
  9. Ex Q.2 (ix)
    Define (i) Sublimation (ii) Triple point.
  10. Ex Q.2 (x)
    Explain the term 'steady state'.
  11. Ex Q.2 (xi)
    Define coefficient of thermal conductivity. Derive its expression.
  12. Ex Q.2 (xii)
    Give any four applications of thermal conductivity in every day life.
  13. Ex Q.2 (xiii)
    Explain the term thermal resistance. State its SI unit and dimensions.
  14. Ex Q.2 (xiv)
    How heat transfer occurs through radiation in absence of a medium?
  15. Ex Q.2 (xv)
    State Newton's law of cooling and explain how it can be experimentally verified.
  16. Ex Q.2 (xvi)
    What is thermal stress? Give an example of disadvantages of thermal stress in practical use?
  17. Ex Q.2 (xvii)
    Which materials can be used as thermal insulators and why?

Solve the following problems

Practice · 15
  1. Solve the following problems.
    Ex Q.3 (i)
    A glass flask has volume 1×10−41 \times 10^{-4} m3^{3}. It is filled with a liquid at 30 ∘^\circC. If the temperature of the system is raised to 100 ∘^\circC, how much of the liquid will overflow. (Coefficient of volume expansion of glass is 1.2×10−51.2 \times 10^{-5} (∘^\circC)−1^{-1} while that of the liquid is 75×10−575 \times 10^{-5} (∘^\circC)−1^{-1}).
  2. Ex Q.3 (ii)
    Which will require more energy, heating a 2.0 kg block of lead by 30 K or heating a 4.0 kg block of copper by 5 K? (slead=128s_{\text{lead}} = 128 J kg−1^{-1} K−1^{-1}, scopper=387s_{\text{copper}} = 387 J kg−1^{-1} K−1^{-1})
  3. Ex Q.3 (iii)
    Specific latent heat of vaporization of water is 2.26×1062.26 \times 10^{6} J/kg. Calculate the energy needed to change 5.0 g of water into steam at 100 ∘^\circC.
  4. Ex Q.3 (iv)
    A metal sphere cools at the rate of 0.05 ∘^\circC/s when its temperature is 70 ∘^\circC and at the rate of 0.025 ∘^\circC/s when its temperature is 50 ∘^\circC. Determine the temperature of the surroundings and find the rate of cooling when the temperature of the metal sphere is 40 ∘^\circC.
  5. Ex Q.3 (v)
    The volume of a gas varied linearly with absolute temperature if its pressure is held constant. Suppose the gas does not liquefy even at very low temperatures, at what temperature the volume of the gas will be ideally zero?
  6. Ex Q.3 (vi)
    In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 ∘^\circC. If maximum temperature in the region is 45 ∘^\circC and the length of each rail section is 10 m, what should be the gap left given that α=1.2×10−5\alpha = 1.2 \times 10^{-5} K−1^{-1} for the material of the rail section?
  7. Ex Q.3 (vii)
    A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the wooden rim and the iron ring are 1.5 m and 1.47 m respectively at room temperature of 27 ∘^\circC. To what temperature the iron ring should be heated so that it can fit the rim of the wheel (αiron=1.2×10−5\alpha_{\text{iron}} = 1.2 \times 10^{-5} K−1^{-1}).
  8. Ex Q.3 (viii)
    In a random temperature scale X, water boils at 200 ∘^\circX and freezes at 20 ∘^\circX. Find the boiling point of a liquid in this scale if it boils at 62 ∘^\circC.
  9. Ex Q.3 (ix)
    A gas at 900 ∘^\circC is cooled until both its pressure and volume are halved. Calculate its final temperature.
  10. Ex Q.3 (x)
    An aluminium rod and iron rod show 1.5 m difference in their lengths when heated at all temperature. What are their lengths at 0 ∘^\circC if coefficient of linear expansion for aluminium is 24.5×10−624.5 \times 10^{-6} /∘^\circC and for iron is 11.9×10−611.9 \times 10^{-6} /∘^\circC
  11. Ex Q.3 (xi)
    What is the specific heat of a metal if 50 cal of heat is needed to raise 6 kg of the metal from 20 ∘^\circC to 62 ∘^\circC ?
  12. Ex Q.3 (xii)
    The rate of flow of heat through a copper rod with temperature difference 30 ∘^\circC is 1500 cal/s. Find the thermal resistance of copper rod.
  13. Ex Q.3 (xiii)
    An electric kettle takes 20 minutes to heat a certain quantity of water from 0 ∘^\circC to its boiling point. It requires 90 minutes to turn all the water at 100 ∘^\circC into steam. Find the latent heat of vaporisation. (Specific heat of water =1= 1 cal/g ∘^\circC)
  14. Ex Q.3 (xiv)
    Find the temperature difference between two sides of a steel plate 4 cm thick, when heat is transmitted through the plate at the rate of 400 k cal per minute per square metre at steady state. Thermal conductivity of steel is 0.026 kcal/m s K.
  15. Ex Q.3 (xv)
    A metal sphere cools from 80 ∘^\circC to 60 ∘^\circC in 6 min. How much time with it take to cool from 60 ∘^\circC to 40 ∘^\circC if the room temperature is 30 ∘^\circC?