Answer to Question #146310 in Physics for Chan

Question

How much water will overflow in a steel pipes hot water heating system containing 75 cubic foot of water? The Hot water heating system is filled with water at 40 °C and then heated to 90 °C. The coefficient of volume expansion for water is 0.00037 per C° or 0.0002 per F°.

Answer 1

The volume increase $\Delta V$ is given by the law of volume termal expansion:

$$\Delta V = \alpha_VV\Delta T$$

Here $\alpha_V = 0.00037\space \degree C^{-1}$ is the coefficient of volume expansion for water, $V = 75 \space ft^3$ is the initial volume, and $\Delta T = 90\degree C - 40\degree C = 50\degree C$ is the increase in temperature. Thus, obtain:

$$\Delta V = 0.00037\cdot 75\cdot 50 = 1.3875\space ft^3$$

Answer. The overflow is $1.3875\space ft^3$.