Question

An environmentally progressive small manufacturer in South Dakota has observed that her gas bill in February (the coldest month of the year) is usually about $900 (for space heating only). She uses a large natural gas space heater whose efficiency is known to be about 89%. She is considering upgrading to a furnace that uses a water source heat-pump with a coefficient of performance of 4.2. The heat-pump operates on 240 VAC electricity. Furthermore, she plans to install a wind turbine to generate enough electricity to power the new heat pump. The turbine will be connected to lead-acid batteries, each 12 VDC, but connected in strings of 5 batteries in series. In planning the wind turbine system, to choose an appropriate turbine and tower height, she needs to estimate the daily DC load that the wind turbine system would need to supply to the inverter on the ground. The inverter’s efficiency (in converting 60 VDC to 240 VAC) is 91%. Estimate the daily DC load (in Wh per day) as input to the inverter to power the heat-pump (for an average day in February). Put a box around this final estimate. By the way, her natural gas costs $6.25/mcf and the energy content of the gas is about 1030 btu/ft³. The electricity she is currently using costs $0.095/kWh.

Answer 1

1mcf = 1000 ft³

1000 Btu/h is approximately 293.1 W

Total gas bill: $900

$6.25/mcf. So total of 900/6.25 = 144 mcf = 144 x 1000 ft³

Total energy content of the gas she buys = 144 x 1000 x 1030 Btu = 148,320,000 Btu = 43,472,592 W h

And the natural gas heater has efficiency of 89%.

So heat generated for space heating = 0.89 x 43,472,592 W h = 38,690,606.9 Wh

Now

4.2*(Work done/Energy supplied ) = 38,690,606.9 Wh

Therefore the energy supplied to heat pump is 9,212,049.26 Wh

This need to be the output of the inverter.

So 100/91 times the above number is the input to the inverter per month = (100/91) * 9,212,049.26 = 10,123,131.1 Wh.

We are asked to find the Daily DC load on the inverter: The above number is for 1 month of February.

Assuming we are not talking about a leap year case: That is the $900 bill for the month of February is for a non leap year.

We get the daily load to be: