Question

HOMEWORK FOR TOMMOROW

Answer 1

(1) Use the formula

(energy E) = (specific heat capacity c) x (mass m) x (change in temperature T)

$E_{thermal} = c\cdot m\cdot \Delta T= 4181 \frac{J}{kg\cdot^\circ C}\cdot 30000kg\cdot 7 ^\circ C=878010000 J\approx 0.88\cdot10^9J = 0.88GJ$

To raise the temperature of the water by 7 degrees Celsius, about 0.88GJ (Gigajoules) of thermal energy is needed.

(2) There are multiple reasons for the observation: Water and concrete have different specific heat capacity, namely that of water is about 4 times higher than one of concrete, so given the same amount of thermal energy, the temperature rises only about a quarter with water as compared to concrete. Another factor in the difference is that while it suffices to heat a relatively thin surface layer of the concrete (i.e., small volume) for it to feel hot to touch, heating the water involves heating a larger volume at a time due to its continuous mixing with lower layers (since it is a liquid with low viscosity).

(3) (a) Install thermal insulation around ducts to minimize thermal energy loss. (b) consider installing multiple heating zones to increase focus of heating to areas that need heating at a given time. (There are many other possible ways, these are just suggestions)