Question

The bulk modulus of water is B = 2.2 x 109 N/m2. What change in pressure ΔP (in atmospheres) is required to keep water from expanding when it is heated from 10.9 °C to 40.0 °C?

Answer 1

Answer:

A change of 160.819 atmospheres is required to keep water from expanding when it is heated from 10.9 °C to 40.0 °C.

Explanation:

The bulk modulus of water ($B$), in newtons per square meters, can be estimated by means of the following model:

$B = \rho_{o}\cdot \frac{\Delta P}{\rho_{f} - \rho_{o}}$ (1)

Where:

$\rho_{o}$ - Water density at 10.9 °C, in kilograms per cubic meter.

$\rho_{f}$ - Water density at 40 °C, in kilograms per cubic meter.

$\Delta P$ - Pressure change, in pascals.

If we know that $\rho_{o} = 999.623\,\frac{kg}{m^{3}}$, $\rho_{f} = 992.219\,\frac{kg}{m^{3}}$ and $B = 2.2\times 10^{9}\,\frac{N}{m^{2}}$, then the bulk modulus of water is:

$\Delta P = B\cdot \left(\frac{\rho_{f}}{\rho_{o}}-1 \right)$

$\Delta P = \left(2.2\times 10^{9}\,\frac{N}{m^{3}} \right)\cdot \left(\frac{992.219\,\frac{kg}{m^{3}} }{999.623\,\frac{kg}{m^{3}} }-1 \right)$

$\Delta P = -16294943.19\,Pa \,(-160.819\,atm)$

A change of 160.819 atmospheres is required to keep water from expanding when it is heated from 10.9 °C to 40.0 °C.