A marine engineering team investigates Boyle’s law for a sample of nitrogen gas trapped inside a high-pressure pneumatic actuator chamber. The pressure p p\,p of the gas in bar\text{bar}bar and its volume V V\,V in L\text{L}L are measured.
The team plots a graph of ln(p/bar)\ln(p / \text{bar})ln(p/bar) against ln(V/L)\ln(V / \text{L})ln(V/L). The equation of the straight line of best fit is:
ln(p/bar)=−1.02ln(V/L)+4.15 \ln(p / \text{bar}) = -1.02 \ln(V / \text{L}) + 4.15 ln(p/bar)=−1.02ln(V/L)+4.15Explain why the gradient of a graph of ln(p/bar)\ln(p / \text{bar})ln(p/bar) against ln(V/L)\ln(V / \text{L})ln(V/L) is expected to be -1 if Boyle’s law is obeyed.
Use the team's line of best fit to calculate the pressure p p\,p of the gas, in bar\text{bar}bar, when its volume V V\,V is 0.35 L. Give your answer to 3 significant figures.
