The heating element of a water heater in an apartment building has a maximum power output of 29 kW. Four residents of the building take showers at the same time, and each receives heated water at a volume flow rate of 12x10-5 m3/s. If the water going into the heater has a temperature of 19°C, what is the maximum possible temperature of the hot water that each showering resident receives?

To determine the maximum possible temperature of the hot water that each showering resident receives, we need to consider the power output of the heating element and the volume flow rate of the water.

First, let's analyze the power output of the heating element. The heating element has a maximum power output of 29 kW. This means it can provide up to 29 kJ of heat energy per second.

Next, let's calculate the amount of heat energy required to heat the water. We can determine this using the formula:

Q = mcΔT

Where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Since we know the volume flow rate of the water, but not the mass, we need to calculate the mass first. The density of water is 1000 kg/m^3, so we can calculate the mass using the formula:

m = density * volume

Given that the volume flow rate is 12x10^-5 m^3/s, we can calculate the mass per second:

m = 1000 kg/m^3 * 12x10^-5 m^3/s

Now that we have the mass per second, we can calculate the heat energy required to increase the temperature of the water. We'll assume the final temperature of the water after heating is the maximum possible temperature:

Q = mcΔT

29 kJ/s = (mass/s) * specific heat capacity * (final temperature - initial temperature)

Finally, rearrange the equation to solve for the final temperature:

final temperature = (29 kJ/s) / [(mass/s) * specific heat capacity] + initial temperature

Plugging in the known values:

final temperature = (29 kJ/s) / [((1000 kg/m^3 * 12x10^-5 m^3/s) * specific heat capacity) + 19°C]

Now, to calculate the specific heat capacity of water, we'll assume it is approximately 4.18 kJ/(kg·°C).

final temperature = (29 kJ/s) / [((1000 kg/m^3 * 12x10^-5 m^3/s) * 4.18 kJ/(kg·°C)) + 19°C]

Now you can plug these numbers into a calculator to find the final result.