A student investigates Boyle’s law for a fixed mass of gas trapped in a syringe. The volume VVV of the gas in cm3\text{cm}^3cm3 and its pressure ppp in kPa\text{kPa}kPa are measured.
The student plots a graph of ln(V/cm3)\ln(V / \text{cm}^3)ln(V/cm3) against ln(p/kPa)\ln(p / \text{kPa})ln(p/kPa). The equation of the straight line of best fit is:
ln(V/cm3)=−0.98ln(p/kPa)+6.95 \ln(V / \text{cm}^3) = -0.98 \ln(p / \text{kPa}) + 6.95 ln(V/cm3)=−0.98ln(p/kPa)+6.95Explain why the gradient of a graph of ln(V/cm3)\ln(V / \text{cm}^3)ln(V/cm3) against ln(p/kPa)\ln(p / \text{kPa})ln(p/kPa) is expected to be −1-1−1 if Boyle’s law is obeyed.
Use the student’s line of best fit to calculate the volume VVV of the gas, in cm3\text{cm}^3cm3, when its pressure ppp is 140 kPa140\text{ kPa}140 kPa. Give your answer to 3 significant figures.
