The table shows data collected for a fixed mass of gas heated at constant pressure. Temperature / K Volume / cm³ Volume / Temperature 250 50 0.20 300 60 0.2...
Question 1 Report
The table shows data collected for a fixed mass of gas heated at constant pressure.
| Temperature / K | Volume / cm³ | Volume / Temperature |
|---|---|---|
| 250 | 50 | 0.20 |
| 300 | 60 | 0.20 |
| 350 | 70 | 0.20 |
| 400 | 80 | 0.20 |
What does the constant ratio in the last column confirm?
Answer Details
The table shows that when a fixed mass of gas is heated at constant pressure, the ratio \( V/T \) (volume divided by kelvin temperature) remains at 0.20 for every data point. A constant ratio \( V/T = k \) means \( V = kT \), which is the mathematical definition of direct proportionality between volume and kelvin temperature.
This is Charles's law: at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. When temperature doubles (from 200 K to 400 K, for example), volume doubles (from 40 cm\(^3\) to 80 cm\(^3\)).
The data cannot confirm a relationship about constant volume (since volume is changing) or about pressure being proportional to volume (since pressure is held constant, not varying). An inverse proportionality would require \( V \times T = \text{constant} \), but \( 250 \times 50 = 12500 \) while \( 400 \times 80 = 32000 \), so that does not hold.
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