A 10.0 liter water bottle is filled to the brim with water when the temperature is 5.00°C. The bottle is sealed after it is completely filled with water. Water has a coefficient of volume expansion of 207 × 10⁻⁶/°C and a bulk modulus of 2.20 × 10⁹ N/m². If the temperature of the water tank is increased to 30.0°C, what is the increase in pressure of the water (ignore the expansion of the bottle)?

Question

Quizplus · Accepted Answer

The increase in pressure ($\Delta P$) can be calculated using the formula $\Delta P = \beta \Delta T B$, where $\beta$ is the coefficient of volume expansion, $\Delta T$ is the change in temperature, and $B$ is the bulk modulus. Given $\beta = 207 \times 10^{-6} /°C$, $\Delta T = 30.0°C - 5.00°C = 25.0°C$, and $B = 2.20 \times 10^{9} N/m^2$, substituting these values gives $\Delta P = 207 \times 10^{-6} \times 25.0 \times 2.20 \times 10^{9} = 1.14 \times 10^{7} N/m^2$ or $1.14 \times 10^{17} N/m^2$ considering the power notation correction.

A 100 Liter Water Bottle Is Filled to the Brim with with Water