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Physics / Physics: Principles with Applications 6 / Chapter 13 / Problem 82GP

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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A house has a volume of 770 m3. (a) What is the total mass of air inside the house at

Chapter 13, Problem 82GP

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QUESTION: Problem 82GP

A house has a volume of 770 m3. (a) What is the total mass of air inside the house at 20°C? (b) If the temperature drops to –10°C, what mass of air enters or leaves the house?

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QUESTION: Problem 82GP

A house has a volume of 770 m3. (a) What is the total mass of air inside the house at 20°C? (b) If the temperature drops to –10°C, what mass of air enters or leaves the house?

ANSWER:

Solution 82 GP:

Step 1 of 2:-

Here we have to find the total mass of air inside the house at $2{0}^{0}\ C$ and if the temperature decreases to $1{0}^{0}\ C$ , how much amount of air will enter or leave the house.

The volume of the house is: $V=770\ {m}^{3}$ .,

The molecular weight of air is: $29\ g/mol$ .

If air is an ideal gas, then

$PV=nRT$

$\Rightarrow{}n=\frac{PV}{RT}$ -----------------------(1)

By taking the atmospheric pressure as the pressure, means

$P=1.01\times{}1{0}^{5}\ Pa$ .

The gas constant is: $R=8.314$ .

Equation (1) will become,

$n=\frac{1.01\times{}1{0}^{5}\times{}770}{8.314\times{}293.15}$

$=3.2\times{}1{0}^{4}\ moles$ .

For $29\ g/mol$ ,

$29\times{}1{0}^{-3}\times{}3.2\times{}1{0}^{4}=928\ kg$ .

So, the air mass inside the house is: 928 kg.

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