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 oC and then heated to 90 oC. The
coefficient of volume expansion for water is 0.00037 per C
o or 0.0002 per Fo
.

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 $1.3875\space ft^3$.