Physics Classes

Tag: Thermal properties of matter

  • Important questions of thermal properties of matter

    Important questions of thermal properties of matter

    This assignment provides all important questions of this chapter , which will be important for examinations point of view.

    1. Briefly describe the various scale of temperature and give the relation between them.

    2.Define coefficient of linear ,area and volume expansion , also find the relation between them.

    3.Show with the help of potential energy diagram that thermal expansion in solid is due to increase in interatomic distance.

    4. What do you mean by the term thermal stress? Derive an expression for the same in case of a road fixed at both ends.

    5. Define heat capacity, molar heat capacity and specific heat capacity also give their units and dimensions.

    6. What do you mean by the term latent heat of fusion and latent heat of vaporization ?

    7.Using P-T diagram of water , discuss the behavior of water when both pressure and temperature are (i) above the triple point (ii) at triple point (iii)below the triple point.

    8. What is thermal conduction ? Discuss the variable and steady state of a rod being heated at one of its ends.

    9. Define the coefficient of thermal conductivity and explain the formula used . Why do metals have higher conductivity then insulator?

    10. Write the expression for the rate of flow of heat energy through a conductor maintained at different temperature at its two ends . Explain the symbols used . Given that heat is measured in joule , derive the units of thermal conductivity.

    11.What is Newton’s law of cooling / how can it be experimentally verified? Plot the graph of log (T-T0) V/S time ‘t’.

    12.Discuss energy distribution in the spectrum of perfectly black body. What conclusion do you derive from this distribution? Also explain the Wine’s displacement law of radiation.

    13. State and explain Stefan’s law . How will you deduce  Newton’s law of cooling from this law?

    14. State and prove Kirchhoff’s law of heat radiation . Explain how Kirchhoff’s law leads to the conclusion that good absorber are good emitters.

    Numericals-

    1. A surveyor uses a steel measuring tape that is exactly 50m long at a temperature of 200C . What is the length on the hot summer day when the temperature is 350C?                                                              coefficient of linear expansion is  1.2 x 10-5K-1. .   [ans-50.009m]

    2. A glass flask with volume 200cm3 is filled to the brim with mercury at 200C . How much mercury overflows when temperature of the system is raised to 1000C ?[α for glass is 0.40x 10-5K-1.and cubical exp. For mercury is 1.2x 10-5K] . Ans-2.7cm3].

    3. A pendulum clock consist of an iron rod connected to a small heavy bob. If it is designed to keep correct time at 200C, how fast or slow will it go in 24 hours at 400C. ( α for iron is 1.2×10-5K-1).                Ans-10.4 sec

    4.At what temperature is the Fahrenheit scale reading equal to(I) half that on the Celsius scale (II)Equal to the reading on Celsius scale?

    5.A faulty thermometer reads 50C in melting ice and 990C in steam . Find the correct temperature in 0F when this faulty thermometer reads 520C.

    6.

    An iron bar of length l1=0.1m, A1=0.02m2, k1= 79w/mK and a brass bar of length l2=0.1m area 0.02m2 and K2=109 W/mK are soldered end to end as shown in fig. the free ends of the iron ball and brass bar maintained at 373K and 273K respectively . Obtain expression for and hence compute (a) the temperature of the junction(b) the equivalent thermal conductivity of the compound bar and (c)the heat current through the compound bar.   Ans-315K ,91.6W/mK, 916W.

    7. A body cools from 700c to 500C in 6 minutes and to 400C in 12 minutes . Find the temperature of the surroundings if cooling occur according to Newton’s law of cooling.        Ans-300C.

    8. A pan filled with hot food cools from 940C to 860C in 2 minutes when the room temperature is 200C . How long will it take to cool from 710C to 690c .    Ans- 42sec.

    9. The energy emitted per second by a black body at 12270C is E . If the temperature of the black body is increased to 27270C , calculate the energy emitted per second in terms of E in the second case. Ans-16E

    10. Calculate the temperature in kelvin scale at which a perfectly black body radiates at the rate of 5.67 W/cm2. Given σ=5.67×10-8W/m2K4.                                  Ans-1000K.

  • Thermal stress

    Thermal stress-

    If we clamp the ends of a rod rigidly to prevent its expansion or contraction and then change the temperature, tensile or compressive stress developed is called thermal stress. The rod like to expand or contract but clamps won’t allow it. As shown in fig.

    To calculate the thermal stress in a clamped rod , we have to find how much the rod would expand if not held rigidly and then find the stress needed to compress it back to its original length. Suppose that the rod with length L0 and cross-sectional area A is held at constant length while the temperature is reduced  causing tensile stress. The fractional change in length if the rod were free to contract would be

     (ΔL/L0 )thermal= αΔT………….(i)

    Both ΔL and ΔT are negative . the tension must increase by an amount F that is just enough to produce an equal and opposite fractional change in length (ΔL/L0 )thermal from the definition of Young’s modulus (Y),

    Therefore Y =( F/A)/(ΔL/L);

    So  (ΔL/L0 )thermal= F/AY …………(II)

    If the length is to be constant , the total fractional change in length must be zero. This means that

    (ΔL/L0 )thermal +  (ΔL/L0 )thermal = 0

    αΔT + F/AY = 0

    F/A = – YαΔT…………………….(III)

    For a decrease in temperature , ΔT is negative , so F and F/A are positive . This means that a tensile force and stress are needed to maintain the length. If ΔT is positive , F and F/A is negative , and the required stress and force are compressive.

    If there are temperature difference within a body , non uniform expansion or contraction will result and thermal stress can be induced .

    You can break a glass bowl by pouring hot water into it . The thermal stress between the hot and cold parts of the bowl exceeds the breaking stress of the glass, causing cracks . The same phenomenon make ice cube crack when dropped into warm water.

  • Change of density with temperature

    Before to go with tis topic students must know the topic thermal expansion of matter, which is one of the most important topic for thermal properties of matter. To learn the topic Thermal expansion of matter CLICK HERE-

    After Completing the topic thermal expansion   students must solve some important questions of thermal expansion of matter, To get (solve)the question  based on this topic CLICK HERE-      

        Change of density with temperature

    The density of a substance is defined as its mass per unit volume of a given mass of a substance changes with temperature while its mass remain the same , the density undergoes a change with the temperature .

    Consider a body of mass m . Let v1 and ƍ1 be its volume and density respectively at temperature t1 and v1and ƍ2 the corresponding values at t2.

    Clearly , mass m= v2ƍ2=v1(1+ƳΔT)ƍ2, where ΔT=t2-t1 ,

    Thus ƍ2 = ƍ1/(1+ƳΔT) = ƍ1(1+ƳΔT)-1. = ƍ1(1-ƳΔT)[ Using Binomial theorem]

    i.e.  ƍ2= ƍ1(1-ƳΔT) [so we can say the density of the material decreases with the rise in temperature].

    Some numericals  for practice based on change of density with temperature are given below .

    1. Coefficient of volume expansion of mercury is 0.18 x 10-3/0C . If the density of mercury at 00C is 13.6g/cc, then its density at 2000C is (a) 13.11g/cc (b)52.11g/cc (c)16.11g/cc (d) 26.11g/cc.

    2. The coefficient of volume expansion of glycerin is 49×10-5/K. The fractional change in density on a 300C rise in temperature is (a)1.47 x 10-2 (b) 1.47 x 10-3 (c) 1.47 x 10-1 (d) 1.47 x 10-4.

  • Numericals based on expansion of matter

    Before to solve these questions students must studied the topic Thermal expansion of matter , to watch the complete notes on this topic click here 

    Important numericals based on expansion of matter-

    1. A surveyor uses a steel measuring tape that is exactly 50m long at a temperature of 200C . What is the length on the hot summer day when the temperature is 350C?                                                              coefficient of linear expansion is  1.2 x 10-5K-1. .   [ans-50.009m]

    2. A glass flask with volume 200cm3 is filled to the brim with mercury at 200C . How much mercury overflows when temperature of the system is raised to 1000C ?[α for glass is 0.40x 10-5K-1.and cubical exp. For mercury is 1.2x 10-5K] . Ans-2.7cm3].

    3. A pendulum clock consist of an iron rod connected to a small heavy bob. If it is designed to keep correct time at 200C, how fast or slow will it go in 24 hours at 400C. ( α for iron is 1.2×10-5K-1).                Ans-10.4 sec

    4. When a strip made of iron (α1) and copper (α2)(α2>α1)is heated then (a)Its length doesn’t change (b)It gets twisted (c)It bends with iron on concave side (d) it bends with iron on convex side.   Ans-c

    5. The volume coefficient of expansion of a liquid is 7 times the volume coefficient of expansion of the vessel. The ratio of absolute and apparent expansion of the liquid is (a) 1/7 (b)7/6 (c)6/7(d)1/6.ans-b

    6. The coefficient of areal expansion of a solid is 2x 10-5 0C-1. Calculate the coefficient of linear expansion.

    7. A bar of iron is 10cm at 200C. At 190Cit will be ( α=11 x10 -5/0C). (a) 11 x10 -6cm longer (b) 11 x10 -6cm shorter (c) 11 x10 -5cm shorter (d) 11 x10 -5cm longer. Ans-c

    8. Coefficient  of volume expansion of mercury is 0.18×10-3/0C. If the density of mercury is 13.6 gm/cc . Then its density at 2000C is (a) 13.11g/cc (b)52.11g/cc (c)16.11g/cc (d) 26.11g/cc. Ans-a

    9. A meter rod of silver at 00C is heated to 1000C Its length is increased by 0.19 cm then the coefficient of volume expansion of the rod is (a) 5.7 x10 -5 /C (b) 0.63 x10 -5/C   (c) 1.9 x 10-5/C (d) 16.1 x10 -5/C . Ans-a

    10. Ratio among coefficient of  linear exp. , area and volume exp. Is (a)1:2:3 (b)3:2:1(c)4:3:2 (d) all of these . Ans-a

    11. A solid ball of metal has a concentric spherical cavity within it . If the ball is heated , the volume of the cavity will (a( increase (b) decrease (c) remain same(d) all are possible. Ans-a

    12. Solid expands on heating because (a) Kinetic energy of the atom increases(b)potential energy of the atom increases (c) total energy of atom increases (d) The potential energy curve is assymetric about the equilibrium distance between neighbouring atoms. Ans-d

  • Thermal expansion

    Thermal expansion

    Most of the material expand when their temperature increases. Then the phenomenon of expansion of material when it is heated is known as thermal expansion.

    1. Linear expansion– When a rod heated then the temperature of the body increases due to which length of the rod increases , this phenomenon is known as the linear expansion .

    Suppose a rod is of length l0 at the initial temperature T0, when its temperature is rises by temperatureT , then the length changes by l. Then the change in length is proportional to original length and rise in temperature,

    i.e.   l α T……………(i)

    And l α l0 ……………..(ii)

    From eq. (i) and (ii)

    l α l0T,

    Or, l = α l0T , where α is the coefficient of linear expansion its unit is K-1 or  ( C0)-1.

    Then the final length l = l0+ l  

    Or, l = l0 + α l0T

    L = l0 ( 1+ α T)………….(iii)

    Area expansion or superficial expansion – When a surface heated then the temperature of the body increases due to which area of the rod increases , this phenomenon is known as the Area expansion .

    Suppose a rod is of length A0 at the initial temperature T0, when its temperature is rises by temperatureT , then the length changes by A. Then the change in area is proportional to original area and rise in temperature,

    i.e.   A α T……………(i)

    And A α l0 ……………..(ii)

    From eq. (i) and (ii)

    A α A0T,

    Or, A = β A0T , where β is the coefficient of Superficial expansion its unit is K-1 or  ( C0)-1.

    Then the final area A = A0+ A  

    Or, A = A0 + β A0T

    A = A0 ( 1+ β T)………….(iii)

    Volume expansion-  When a rod heated then the temperature of the body increases due to which volume of the rod increases , this phenomenon is known as the volume expansion .

    Suppose a rod is of length V0 at the initial temperature T0, when its temperature is rises by temperatureT , then the length changes by V. Then the change in length is proportional to original length and rise in temperature,

    i.e.   V α T……………(i)

    And V α V0 ……………..(ii)

    From eq. (i) and (ii)

    V α V0T,

    Or, V = Ÿ V0T , where Ÿ is the coefficient of linear expansion its unit is K-1 or  ( C0)-1.

    Then the final length V = V0+ V  

    Or, V = V0 + Ÿ V0T

    V = V0 ( 1+ Ÿ T)………….(iii)

    Relation between linear, area and volume expansion (α,β and Ÿ )

    2α=β; and 3α=Ÿ

    Or , α = β/2=Ÿ/3 .

    To solve the important questions based on this topic CLICK HERE-

    To solve the important questions based on the topic Temperature and thermometers CLICK HERE-

  • Important numericals on temperature and thermometer (Temperature scale)

    Temperature is a relative measure of hotness or coldness of a body. An object at a higher temperature is said to be hotter than the one at a lower temperature. The S.I. unit of temperature is Kelvin(K).

    (We must keep it in our mind that , Heat and temperature are not the same thing , heat is the flow of energy , whereas temperature is a microscopic property of body.)

    Important numericals on Thermal properties of matter.

    A- Numericals based on temperature and( temperature scale)

    Formula used in the following questions-

        [ ( Tc-0)/100 = (tF-32)/180 = (tK-273)/100 = (tr-F.P.)/(B.P. –F.P.) ]

    temperature scales

    1. An object has a temperature of 500F. What is the temperature in degrees Celsius and in Kelvin?

     [Ans- 100C, 283.15K]

    2. A pan of water is heated from 250C to 800C. What is the change in the temperature in Kelvin scale and on the Fahrenheit scale?   [Ans- 55K,990F]

    3. A faulty thermometers reads 50C in melting ice and 990C in steam .Find the correct temperature in 0F when this faulty thermometer reads 520C.    [Ans-1220F]

    4. At what temperature is the Fahrenheit scale reading equal to half that on the Celsius scale?             [Ans-0.6670F]

    5. At what temperature the reading on both Celsius and Fahrenheit scale remain the same? [Ans—400C]

    6. The triple points of neon and carbon dioxide are 24.57K and 216.55K respectively. Express temperatures on the Celsius and Fahrenheit scale. [Ans—248.580C, -56.60C, -415.440F,-69.880F].

    After solving these questions students have to learn- Thermal expansion, CLICK HERE-

    To solve the questions based on the thermal expansion-CLICK HERE