When you heat the air in a house, some air escapes because the pressure inside t

Question

When you heat the air in a house, some air escapes because the pressure inside the house must remain the same as the pressure outside. Suppose you heat the air from 10 degrees C to 30 degrees C. What fraction of the mass of air originally inside will escape? If the house were completely airtight, the pressure would have to increase as you heated the house. Suppose that the initial pressure inside the house is 1.00 atm. What is the final pressure? What force does this excess inside pressure exert on a window 1.0 m high and 1.0 m wide? Do you think the window can withstand this force?

Explanation / Answer

in first case pressure and volume is constant

n1t1 = n2t2

n1 * 283 = n2 * 303

n1 /n2 = 303/283

fraction of mass of air that escapes = (n1 - n2)/n1

=1-(n2/n1)

= 1- (283/303)

= 20/303 = 0.066 or we can say that 6.6%

in second case

no. of moles of air and volume is constant

p1/t1 = p2/t2

p2 = (1/283)*303

p2 = 1.071 atm

force on window = 1.071 * 1.01325 ×105 * 1 * 1 = 1.085 * ×105 N

yes the window can withstand the force because sometimes in normal conditions also the pressure is more than 1 atm and the windows withstand it.

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