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If the temperature of a gas is constant, the pressure that the gas exerts varies inversely with the volume. If a gas, at constant temperature, has a volume of 76 in. cubed when the pressure is 16 pounds per square inch, what will the volume be when thepressure is 64 pounds per square inch?O A 9 in 3O e. 13. in 3O C. 19 inOD. 38 in.OE. 304 in 3

Answer :

Here, the pressure the gas exerts varies inversely with the volume.

Where the constant, k = temperature of the gas

Let p represent the pressure the gas exerts

Let v represent the volume.

Since the relationship here is an inverse variation, we have the formula:

[tex]p=\frac{k}{v}[/tex]

Given:

v = 76

p = 16

Let's solve for k:

[tex]\begin{gathered} 16=\frac{k}{76} \\ \\ 76\times16=k \\ \\ k=76\times16 \\ \\ k=1216 \end{gathered}[/tex]

Now, let's find the volume when the pressure is 64.

Substitute 1216 for k and 64 for p, to find the volume:

[tex]\begin{gathered} p=\frac{k}{v} \\ \\ 64=\frac{1216}{v} \\ \\ v=\frac{1216}{64} \\ \\ v=19in^3 \end{gathered}[/tex]

Therefore, when the pressure is 64 pounds per square inch, the volume will be 19 in. cubed.

ANSWER:

[tex]C.19in^3[/tex]

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