Question

use the inverse variation equation to fill in the table.
p = \frac{8.31}{v}

volume (liters)	pressure (kilopascals)
b	0.4
415.5	c

a = \square, b = \square, c = \square

Explanation:

Step1: Find \( a \) when \( V = 83.1 \)

Substitute \( V = 83.1 \) into \( p=\frac{8.31}{V} \). So \( a=\frac{8.31}{83.1} \). Simplify, \( \frac{8.31}{83.1}=0.1 \).

Step2: Find \( b \) when \( p = 0.4 \)

Substitute \( p = 0.4 \) into \( p=\frac{8.31}{V} \), we get \( 0.4=\frac{8.31}{b} \). Solve for \( b \): \( b=\frac{8.31}{0.4}=20.775 \).

Step3: Find \( c \) when \( V = 415.5 \)

Substitute \( V = 415.5 \) into \( p=\frac{8.31}{V} \). So \( c=\frac{8.31}{415.5} \). Simplify, \( \frac{8.31}{415.5}=0.02 \).

Answer:

\( a = 0.1 \), \( b = 20.775 \), \( c = 0.02 \)