GS-1 Physical Sciences Question 44

[scott.glea1906]

This question violates the equation of continuity which states that the density of a substance will not change in response to changes in temperature or pressure...?

[mcat_premed3832]

Actually, you are focusing on a specific application of the Continuity Equation: incompressible fluids. Water is normally approximated as an incompressible fluid but in this problem, we are told of "an accurate weighing apparatus" and, though the difference may be small, it is the only answer that, flows? (sorry for that!)

The general structure of the continuity equation does take into account that the density of a fluid changes in space as it flows through a system:

(rho)(A)(v) is constant

Thus

(rho)1 (A)1 (v)1 = (rho)2 (A)2 (v)2

The special case is for an incompressible fluid: given that the density does not change (thus this factor is removed from the equation) then Av is constant, blah blah (the question ensues).


Below you will find information which is not needed for the MCAT:

Water (molecule - Wikipedia, http://en.wikipedia.org/wiki/Water_(molecule)

The compressibility of water is a function of pressure and temperature. At 0 °C in the limit of zero pressure the compressibility is 5.1×10-5 bar−1. In the zero pressure limit the compressibility reaches a minimum of 4.4×10-5 bar−1 around 45 °C before increasing again with increasing temperature. As the pressure is increased the compressibility decreases, being 3.9×10-5 bar−1 at 0 °C and 1000 bar. The bulk modulus of water is 2.2×109 Pa. The low compressibility of non-gases, and of water in particular, leads to them often being incorrectly labelled as incompressible (later changed to: leads to their often being assumed as incompressible). The low compressibility of water means that even in the deep oceans at 4000 m depth, where pressures are 4×107 Pa, there is only a 1.8% decrease in volume.


Fine, R.A. and Millero, F.J. (1973). "Compressibility of water as a function of temperature and pressure". Journal of Chemical Physics 59 (10): 5529.