Question

the graph shows the volume of a sample of gas as a function of temperature. use the graph to determine the volume of the sample at a temperature of 225 k. graph: volume (ml) on y - axis (0, 250, 500, 750, 1000), temperature (k) on x - axis (0, 50, 100, 150, 200, 250, 300, 350, 400), straight line from (0,0) with data points. answer:

Explanation:

Step1: Analyze the graph's trend

The graph is a straight line passing through the origin, so it represents a direct proportionality \( V = kT \) (where \( V \) is volume, \( T \) is temperature, and \( k \) is the constant of proportionality). We can find \( k \) using a point on the line. Let's take a point, for example, when \( T = 300 \, \text{K} \), from the graph, the volume \( V \) seems to be around \( 600 \, \text{mL} \) (by estimating the points). So \( k=\frac{V}{T}=\frac{600}{300} = 2 \, \text{mL/K} \).

Step2: Calculate volume at 225 K

Using the formula \( V = kT \), with \( k = 2 \, \text{mL/K} \) and \( T = 225 \, \text{K} \), we get \( V=2\times225 = 450 \, \text{mL} \). Alternatively, by directly reading from the graph (since it's a straight line, we can interpolate). The x - axis (temperature) has intervals, and at \( T = 225 \, \text{K} \), moving up from the x - axis to the line and then left to the y - axis (volume), we can see that the volume should be \( 450 \, \text{mL} \) (since the slope is consistent, for every 1 K increase in temperature, volume increases by 2 mL, as seen from \( T = 0, V = 0 \); \( T = 100, V = 200 \); \( T = 200, V = 400 \); so at \( T = 225 \), \( V = 450 \)).

Answer:

\( 450 \, \text{mL} \)