A student uses a syringe to compress air at constant temperature. She records volume and the force she applies to the plunger. Volume / cm³ Force on plunger...
Question 1 Report
A student uses a syringe to compress air at constant temperature. She records volume and the force she applies to the plunger.
| Volume / cm³ | Force on plunger / N |
|---|---|
| 40 | 10 |
| 20 | 20 |
| 10 | 40 |
| 5 | 80 |
The cross-sectional area of the plunger is constant. What relationship between force and volume does the data show?
Answer Details
Examine the data: when the volume halves, the force doubles. Volume goes 40, 20, 10, 5 while force goes 10, 20, 40, 80. The product \( F \times V \) is constant: \( 10 \times 40 = 400 \), \( 20 \times 20 = 400 \), \( 40 \times 10 = 400 \), \( 80 \times 5 = 400 \). A constant product \( FV = k \) means \( F = k/V \), the definition of inverse proportionality.
This follows from Boyle's law. At constant temperature, \( PV = \text{constant} \). Since the plunger has a fixed cross-sectional area \( A \), pressure \( P = F/A \), so \( (F/A) \times V = \text{constant} \), giving \( F \times V = \text{constant} \). Force is therefore inversely proportional to volume.
Direct proportionality would require force and volume to increase together (they do the opposite). Proportionality to volume squared would not produce a constant \( FV \) product. And force is clearly not independent of volume - it changes markedly as volume changes.
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