Suppose your bedroom is 18 ft long and 15 ft wide, and the distance from floor to ceiling is 8 ft 6 in. You need to know the volume of the room in metric units for some scientific calculations. (a) What is the room's volume in cubic meters? In liters? (b) What is the mass of air in the room in kilograms? In pounds? (Assume the density of air is 1.2 g/L and that the room is empty of furniture.)
Solution Summary: The author explains that density is the relationship between the mass of a substance and how much space it takes up (volume).
Suppose your bedroom is 18 ft long and 15 ft wide, and the distance from floor to ceiling is 8 ft 6 in. You need to know the volume of the room in metric units for some scientific calculations.
(a) What is the room's volume in cubic meters? In liters?
(b) What is the mass of air in the room in kilograms? In pounds? (Assume the density of air is 1.2 g/L and that the room is empty of furniture.)
(a)
Expert Solution
Interpretation Introduction
Interpretation: The volume of the room in cubic meters and liters has to be given.
Concept Introduction:
Density: is a characteristic property of a substance. The density of a substance is the relationship between the mass of the substance and how much space it takes up (volume).
Density = MassVolume
Answer to Problem 54RGQ
Volume in liters is 65.41×103 L
Explanation of Solution
The volume of the room in cubic meters and litres is given,
Calculate the volume of room:_Volume of a room is l×h×w Given: length = 18ft = 5.4864m , wide = 15 ft = 4.572 m, height = 8 ft 6 in = 2.5904 mVolume = 5.49 m ×4.6 m ×2.59 m = 65.41m3Conversion of units:_Given: Volume = 65.41m3Known: 1 m3 = 103 LWhereas,65.41m3 is = 65.41m3×103 L1 m3=65.41×103 L =65.41×103 L.
The volume in cubic liters is 65.41×103 L
(b)
Expert Solution
Interpretation Introduction
Interpretation: The volume of the room in cubic meters and liters has to be given.
Concept Introduction:
Density: is a characteristic property of a substance. The density of a substance is the relationship between the mass of the substance and how much space it takes up (volume).
Density = MassVolume
Answer to Problem 54RGQ
Mass of air in kilogram is 78.492Kg and in pounds is 0.1730pounds.
Explanation of Solution
The mass of air is calculated as,
Calculate the mass of air:_Given: Density = 1.2 g/L ; Volume = 65.41×103 LKnown: Density = MassVolumeWhereas,Mass = Density×Volume = 1.2 g/L× 65.41×103 L =78.492×103g.Conversion of units:_Known:1g = 0.001 kgWhereas, 78.492×103g is,= (78.492×103g)(0.001 kg)1g = 78.492Kg.Conversion of units:_Known:1g = 0.00220462 poundWhereas, 78.492×103g is,= (78.492×103g)(0.00220462 pound)1g = 0.1730pounds.
The obtained mass in kilograms and pounds are shown above.
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