Question

Make and Use Graphs For every 6°C drop in temperature, the air pressure in a car’s tires goes down by about 1 psi (14.7 psi = 1.00 atm). Make a graph illustrating the change in tire pressure from 20°C to -20°C (assume 30.0 psi at 20°C).

Short answer

To create a graph illustrating the change in tire pressure from 20°C to -20°C, first calculate the psi decrease for each 6°C temperature drop. The initial tire pressure is 30 psi at 20°C. Calculate the tire pressure at 14°C, 8°C, 2°C, -4°C, -10°C, and -16°C by subtracting 1 psi for each 6°C drop in temperature. Next, plot these points on a graph with the x-axis representing temperature in °C and the y-axis representing tire pressure in psi. Finally, connect the points with a line, showing the change in tire pressure as the temperature drops from 20°C to -20°C.

Step-by-step solution

Calculate the temperature drop and corresponding psi decrease.

Determine the temperature drop from 20°C to -20°C, which is 40°C (20 - (-20) = 40). Divide the temperature difference by 6°C to find the corresponding psi decrease, which is 40/6 ≈ 6.67 psi. Since we want to find the tire pressure at different temperatures within the given range, we'll round this psi value to the nearest integer.

Calculate the tire pressure at different temperatures.

Calculate the tire pressure at 14°C, 8°C, 2°C, -4°C, -10°C, and -16°C by subtracting the psi decrease for each 6°C drop in temperature from the initial tire pressure at 20°C, which is 30 psi. 20°C: 30 psi 14°C: 30 - 1 = 29 psi 8°C: 29 - 1 = 28 psi 2°C: 28 - 1 = 27 psi -4°C: 27 - 1 = 26 psi -10°C: 26 - 1 = 25 psi -16°C: 25 - 1 = 24 psi

Plot the tire pressure with the corresponding temperature on a graph.

With the calculated tire pressures at different temperatures, plot these points on a graph with the x-axis representing the temperature in °C and the y-axis representing the tire pressure in psi. - x-axis: -20°C, -16°C, -10°C, -4°C, 2°C, 8°C, 14°C, 20°C - y-axis: 24 psi, 25 psi, 26 psi, 27 psi, 28 psi, 29 psi, 30 psi

Connect the points with a line.

Create a line connecting the points in the graph to illustrate the change in tire pressure as the temperature drops from 20°C to -20°C. The line should have a negative slope, indicating a decrease in tire pressure as the temperature decreases. By following these steps, the graph should represent the change in tire pressure within the given temperature range.

Key concepts

Temperature and Pressure Correlation

Understanding the relationship between temperature and pressure is important in many scientific fields, including chemistry and physics. This correlation, typically found in ideal gases, can also be observed in everyday life—such as in the air pressure of car tires.
In our exercise example, the correlation between temperature decrease and tire pressure decrease is quantified: for every 6°C drop in temperature, the tire pressure decreases by 1 psi. This direct relationship is an application of the combined gas law, which relates pressure, volume, and temperature. An important point to note is that the volume and the amount of air within the tire are assumed to be constant in these types of problems, allowing the focus to remain on temperature and pressure alone.
By plotting this relationship on a graph, it becomes easier to visualize and predict the behavior of tire pressure in response to temperature changes. When the temperature drops, molecules within the tire move slower and collide with the tire walls less forcefully, causing a decrease in pressure. This can be seen as a downward trend in a graph where temperature is plotted against pressure.

Creating a Graph in Chemistry

Graphs are invaluable tools in chemistry for displaying data in a clear and interpretable way. To create a graph that illustrates a scientific concept effectively, several steps should be considered.

• Identify the variables: Determine what you are comparing. In our case, it's temperature versus pressure.
• Select the graph type: Choose a graph that suits the data. A line graph is common for showing trends or changes over a range of values.
• Scale the axes: Make sure the scale is appropriate for the range of your data. In this example, the x-axis ranges from -20°C to 20°C and the y-axis from 24 psi to 30 psi.
• Plot the data: Mark the data points accurately on the graph.
• Draw the trend: Connect the points to show the pattern or trend. Our trend is a linear decrease in pressure with a decrease in temperature.

By following these steps, the resulting graph would be a simple line graph with temperature on the x-axis and pressure on the y-axis, clearly showing the inverse relationship between these two variables.

Interpreting Data in Chemistry

Interpretation of data is a crucial skill in chemistry that allows us to extract meaning from the data obtained through experiments or calculations. In our exercise, interpreting the graph involves understanding how the pressure of air in the tires changes with temperature.
First, examine the trend displayed by the line. A downward slope indicates an inverse relationship—if one variable increases, the other decreases. In our scenario, as temperature decreases, pressure also decreases. This trend continues uniformly for each 6°C drop in temperature, with a corresponding decrease of 1 psi in pressure.
This linearity suggests a consistent ratio between temperature change and pressure change, providing the student with not only quantifiable data points but also an underlying principle that could predict the pressure at other temperatures not explicitly calculated.
Moreover, interpreting graph data is not only about understanding past behaviour but also predicting future outcomes. With the provided graph, one might estimate the tire pressure at temperatures not listed in the exercise, assuming the linear relationship holds. This extrapolation is fundamental in applying theoretical knowledge to real-world applications.