Calculate the weight of air at 20^∘ C in a room that measures 5.00 ×4.50 ×3.25 m . Give your ans

Calculate the weight of air at 20^∘ C in a room that...

Key Concepts

Weight Calculation

Weight is the force exerted by gravity on a mass. To calculate the weight of an object, the mass is multiplied by the gravitational acceleration. This concept links the fundamental properties of matter with the forces acting upon it in a gravitational field.

Mass Calculation

Mass is obtained by multiplying the density of a substance by its volume. This straightforward calculation is vital for transitioning from a volumetric analysis to one that considers the actual amount of matter present, which is then used to determine weight.

Unit Conversion

Unit conversion involves translating measurements from one system to another, such as from newtons (SI unit of force) to pounds (imperial unit of force). This step ensures that the final answer is accessible and usable in different contexts, adhering to the appropriate units of measurement.

Volume Calculation

The volume of a three-dimensional space is determined by multiplying its length, width, and height. This concept is essential in problems involving the quantity of a substance distributed throughout a space, as it provides a basis for subsequent computations such as mass and weight.

Density

Density is a measure of how much mass is contained within a given volume of a substance. In the context of air, the density varies with temperature and pressure, and knowing the density is crucial for converting a volume measurement into mass.

Transcript

00:01 This problem asks us to find the weight in both newtons and pounds of a mass of air at 20 degrees celsius, and we're given the dimensions of that mass of air.

00:10 In order to solve this problem, there's a few things that we're going to need to know, in addition to what's laid out in the problem.

00:16 We know that the density of the material is equal to its mass divided by its volume.

00:22 We can look up that the density of air at 20 degrees celsius, which is what's relevant to our problem, is equal to 1 .1.

00:31 2 kilograms per cubic meter.

00:36 We can also know that we're going to need to convert whatever mass we figure out from that density equation into a weight.

00:43 To deal with that in newtons, we can know that weight in newtons is equal to mass in kilograms times the acceleration due to gravity in meters per second squared.

00:52 And then we can also take that weight in newtons and use the fact that one newton is equal to 0 .2242.

01:02 Pounds and those are provided by our text.

01:05 We can look that conversion up should we need to.

01:08 The first thing we're going to need to do is we're going to need to find the volume of this air.

01:13 To do so, we're just going to multiply out our three dimensions.

01:17 We're given length, width, and height.

01:19 So to find volume of our air, i'm going to do 5 .00 times 4 .50 times 3 .25 meters.

01:28 I do that and i end up with a volume of 73 .125 meters.

01:35 I'm not going to round quite yet until i get to the end of my problem.

01:39 I also do already know from the information i gathered before i started my problem that the density of air is equal to 1 .2 kilograms per cubic meter.

01:51 And now what i'm going to do is i'm going to rearrange our density equation so that i can solve for mass...

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