The problem provided involves the linear function for gas volume expansion:

$V(T) = 0.133T + 31$

where $V(T)$ represents the volume in cubic centimeters, and $T$ is the temperature in degrees Celsius.

Let's break down the problem:

a) Evaluate $V(0)$:

This requires us to find the volume when the temperature is $T = 0$. Simply substitute $T = 0$ into the given equation: $V(0) = 0.133(0) + 31 = 31 \text{ cubic centimeters}.$

b) If the temperature increases by 40 degrees, by how much does the volume increase?

To find how much the volume increases when the temperature increases by 40 degrees, note that the coefficient of $T$, which is 0.133, gives the rate of change of volume with respect to temperature. Thus, the volume increase is: $\Delta V = 0.133 \times 40 = 5.32 \text{ cubic centimeters}.$

c) What is the volume of gas when the temperature is 40 degrees?

Substitute $T = 40$ into the equation to find the volume at 40 degrees: $V(40) = 0.133(40) + 31 = 5.32 + 31 = 36.32 \text{ cubic centimeters}.$

Would you like more details on any part of this, or have any questions?

Here are 5 related questions to practice with:

1. What is the volume when the temperature is 100 degrees Celsius?
2. How does the volume change if the temperature decreases by 10 degrees Celsius?
3. What is the slope of the line representing $V(T)$, and what does it physically represent?
4. What is the temperature when the volume is 50 cubic centimeters?
5. If the volume of gas is 31 cubic centimeters, what is the temperature of the gas?

Tip: In linear functions, the slope tells you how much the dependent variable (volume) changes per unit increase in the independent variable (temperature).