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Heating effects

• Air in a cylinder is compressed to one-tenth of its original volume without change in temperature. What happens to its pressure? Imagine now that a valve is opened in order to restore the initial pressure value. What percentage of the molecules have escaped?

Consider a 40,000 km steel pipe in the shape of a ring that fits snugly all around the circumference of the Earth. We are heating now the ring so its temperature increased by 1 degree C. Now, the pipe will no longer be snug. How high the ring will now stand above ground level? (Make as many simplifications as necessary). Data: Coefficient of linear expansion for steel is 11*10-6 /degree C. This means, for example, that a 1-meter bar of steel that increases its temperature by 1 degree C will expand 11*10-6 meters (11 micrometers)

Farmers resort to spraying fruit trees with water before a frost to protect the fruit from freezing. Using the concepts learned in this module, discuss why this does or does not work.

• An electric fan not only does not decrease the temperature of the air, but it actually increases air temperature. How can you then explain that you are cooled by a fan

Solution Preview

1.
Initial volume, V1 = V
Final volume, V2 = V/10
Number of moles = n
Constant temperature = T
Initial pressure, P1 = P
Final pressure, P2 = ?

Because, P1.V1 = P2.V2
=> P*V = P2*V/10
=> P2 = 10P

Now, let us assume on opening the valve, n' moles escape, and pressure becomes P1(=P)

Remaining moles = n-n'

Because,
P*V = n*R*T
For remaining gas:
P*V/10 = ...

Solution Summary

A few problems useful to understand some of the concepts of heating - ideal gas processes, expansion of metals, saving fruits from frost, and working of fan.

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