Question

A geothermal aquifer supplies hot water at a temperature of 70 deg C at a flow rate of 10L/s. The hot water is used in a district heating system at a temperature of 40 deg C. It is assumed that all the thermal energy can be transferred through a heat exchanger. The geothermal aquifer is used 150 days each year. Calculate the amount of heat used for heating during the year.

Calculate the amount of oil necessary to get the same amount of heat assuming an efficiency of 80% for the fuel-fired boiler. One ton of oil responds to 42 GJ.

Answer 1

This is a question based on heat transferred

we know that

Q = m*C*change in temperature

we need to find mass (as it is not given directly in the question)

How do we find it ?

m = density * flow rate * time (if we use the units , then we see that we are left with only Kg which is the unit of mass, so yes, we can use this equation)

We need density of water at 70 ^oC. It would have been great if question gave this value.

I found from textbook, that at 70 ^oC, density will be around 977.74 Kg / m³. I still want you to check. However, the method is just fine and accurate.

flow rate is given in L/s. we need to convert in m³ / s

so,

10 L/s = 0.01 m³ / s

C = 4194 J/Kg ^oC (specific heat of water)

time is 150 days or 12960000 seconds

so,

Q = m*C*change in temperature

Q = 977.74 * 0.01 * 4194 * 12960000 * (70 - 40)

Q = 1.594e13 J

so, this is the heat required in a year.