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Thermometry

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#### 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.