The variation of absolute pressure P with depth h below the free surface of an unknown liquid is plotted on a graph. The graph is a straight line that gives P = 1 10^5 Pa at h = 0 m, and P = 2.2 10^5 Pa at h = 10 m. Assuming the acceleration due to gravity g = 10 m/s ^2 , what is the density of the liquid?

Step-by-step solution

The absolute pressure P at a depth h is given by the equation: P = P_ atm + g h This represents a linear equation of the form y = c + mx , where the slope of the P versus h graph is m = g . From the given data, the slope is: P h = 2.2 10^5 - 1 10^5 10 - 0 P h = 1.2 10^5 10 = 1.2 10^4 Pa/m Equating this slope to g : g = 1.2 10^4 10 = 12000 = 1200 kg/m ^3 Using P/h at h=10 without subtracting the intercept leads to the incorrect 2200 kg/m ^3 . Answer: 1200 kg/m ^3