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Thermometry

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Q.

In column 1, a uniform bar of uniform cross-sectional area under the application of forces is shown in the figure and in Column 2, some effects/phenomena are given. Match the entries of Column 1 with the entries of Column 2.

                   Column 1

                Column 2

 (A)

 

 (p)

 Uniform stress developed in  the rod

 (B)

   

 (q)

 Non-uniform stresses  developed in the rod

 (C)

    

 (r)

 Compressive stress  developed

 (D)

    

 (s)

 Tensile stresses developed

 

Q.

A copper rod (initially at room temperature ) of non-uniform cross section is placed between a steam chamber at  and ice water chamber at  A and B are cross sections as shown in Fig. Then match the statement in Column I with results in Column II comparing only between cross sectionA and B, (The mathematical expressions in Column I have their usual meanings in heat transfer.)

                                         

                   Column-1

                Column-2

 (A)

 Initially rate of heat flow    will be

 (p)

 Maximum at section A

 (B)

 At steady state rate of heat  flow  will be

 (q)

 Maximum at section B

 (C)

 At steady state temperature  gradient  will be

 (r)

 Minimum at section B

 (D)

 At steady state rate of  change of temperature  will be

 (s)

 Same for all section

 

Q.

In a container of negligible mass ‘m’ grams of steam at  is added to 100 g of water that has temperature  If no heat is lost to the surroundings at equilibrium match the items given in Column 1 with Column 2.

                   Column 1

                Column 2

 (A)

 Mass of steam in the mixture,  ifm = 20 g (in g)

 (p)

 114.8

 (B)

 Mass of water in the mixture,  ifm = 20 g (in g)

 (q)

 76.4

 (C)

 If m = 20 g, final temperature of  the mixture 

 (r)

 5.2

 (D)

 If m = 10 g, final temperature of  the mixture 

 (s)

 100

 

Q.

A piece of metal of density  floats on mercury of density  The coefficients of expansion of the metal and mercury are  respectively. The temperatures of both mercury and metal are increased by  Then match the following :

                   Column 1

                Column 2

 (A)

  

 (p)

 No effect on fraction of solid  submerged in mercury

 (B)

  

 (q)

 Fraction of the volume of metal  submerged in mercury increases

 (C)

  

 (r)

 The solid sinks

 

 

 (s)

 The solid lifts up

 

Q. A railway track (made of iron) is laid in winter when the average temp. is 18C. The track consists of sections of 12.0m placed one after the other. How much gap should be left between two such sections so that there is no compression during summer when the temp goes to 48C? Coeff of linear expansion of iron=11*10^-6/C
I have tried solving the above question by using the formula: (delta L)=L (alpha)(delta T) and then tried multiplying the expansion by two, as the gap is between two such sections. But I'm not getting the correct answer. Please explain..?

you will get delta L= 0.003960 m on solving which is equal to approx 4cm which will be your final answer , you don't have to multiply by 2 since we are considering expansion from one end only in this formula. how ever there will be expansion from both end equally ideally but in that case we will take delta L = 20cm and then multiply by 2 ​

Q. Which is the smallest temperature?

To understand this, we will convert all given temperatures to Kelvin.

1˚C = 274.15 K

The temperature in K = Given temperature in ˚C + 273.15

Here, we are given temperature in ˚C as 1.

So, the temperature in K is

1 + 273.15 = 274.15 K

1˚F = 256 K

This is because, temperature in K = Given temperature in ˚F + 459.67

Here, the given temperature in ˚F= 1

So, temperature in K= =256K

So, 1˚C > 1˚F > 1 K

So, 1 Kelvin is the smallest temperature.

Q. If the metal sphere attached at the end of the copper rod is made of brass, whole thermal conductivity is Kb < K?

The temperature T will change to a new value. The transmitted thermal energy will be the same.