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Answer :
To determine the energy input for a 4-ton air conditioner with an EER of 12.0, we must convert the cooling capacity from BTUs to joules and then calculate power input in watts. The total energy input in joules is then obtained by multiplying the hourly power input by the number of seconds in an hour. The cost is calculated by converting energy input to kilowatt-hours and multiplying by the electricity rate.
When calculating the energy input required for an air conditioner with an energy efficiency rating (EER) of 12.0 BTU per watt-hour, we first translate the cooling capacity into watts. Using the conversion factor 1 BTU = 1055.06 joules, we find that 48,000 BTU is equivalent to 5.06×107 joules. Therefore, the hourly power input needed by a 4-ton air conditioner can be calculated as follows:
Energy input (watts) = Total energy transferred (joules) / EER
This gives us an hourly power input in watts. Since 1 watt is equal to 1 joule per second, we can find the total energy input in joules by multiplying the power input by the number of seconds in an hour (3600 seconds).
To calculate the cost, we use the given rate of 10.0 cents per 3.6×106 joules (1 kilowatt-hour). Therefore, to find the cost of operating the air conditioner for one hour, we divide the energy input in joules by 3.6×106 joules to get the number of kilowatt-hours, and then multiply by the cost per kilowatt-hour.
Finally, we can discuss whether this cost is realistic by comparing it to the typical costs of running household appliances, taking into account the price of electricity and the air conditioner's energy efficiency.
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