Question

1. competency check the table shows the effect of temperature on the volume of a specific gas.

temperature (°c)	volume (ml)
20	862
30	877
40	892

a) graph the relation.
b) state an equation representing the relationship between volume and temperature.
c) what would the volume of gas be at a temperature of 50 °c?
d) at what temperature would the volume of gas be 757 ml?

Explanation:

Step1: Identify linear relationship

First, confirm the relationship is linear by checking the constant rate of change. For temperature increase of 10°C, volume increases by 15 mL, so slope $m = \frac{15}{10} = 1.5$.

Step2: Find the y-intercept

Use point-slope form $V - V_1 = m(T - T_1)$ with $(T_1, V_1) = (10, 847)$:
$V - 847 = 1.5(T - 10)$
Simplify to slope-intercept form:
$V = 1.5T - 15 + 847$
$V = 1.5T + 832$

Step3: Calculate volume at 50°C

Substitute $T = 50$ into the equation:
$V = 1.5(50) + 832$
$V = 75 + 832$

Step4: Calculate temperature for 757 mL

Substitute $V = 757$ into the equation and solve for $T$:
$757 = 1.5T + 832$
$1.5T = 757 - 832$
$1.5T = -75$
$T = \frac{-75}{1.5}$

Answer:

a) (Graph: Plot the points (10, 847), (20, 862), (30, 877), (40, 892) on a coordinate plane with Temperature (°C) on the x-axis and Volume (mL) on the y-axis, then draw a straight line through them.)
b) $V = 1.5T + 832$
c) 907 mL
d) $-50^\circ\text{C}$