A marine researcher investigates the behavior of a small air bubble trapped in a flexible diagnostic chamber of a deep-sea vehicle. The volume V V\,V of the bubble in mm3\text{mm}^3mm3 and its pressure P P\,P in MPa\text{MPa}MPa are recorded during a controlled descent.
The researcher plots a graph of ln(V/mm3)\ln(V / \text{mm}^3)ln(V/mm3) against ln(P/MPa)\ln(P / \text{MPa})ln(P/MPa). The equation of the straight line of best fit obtained is:
ln(V/mm3)=−1.03ln(P/MPa)+5.24 \ln(V / \text{mm}^3) = -1.03 \ln(P / \text{MPa}) + 5.24 ln(V/mm3)=−1.03ln(P/MPa)+5.24Explain why the gradient of a graph of ln(V/mm3)\ln(V / \text{mm}^3)ln(V/mm3) against ln(P/MPa)\ln(P / \text{MPa})ln(P/MPa) is expected to be -1 if Boyle’s law is obeyed.
Use the researcher’s line of best fit to calculate the volume V V\,V of the gas bubble, in mm3\text{mm}^3mm3, when the pressure P P\,P is 6.20 MPa. Give your answer to 3 significant figures.
