How do you calculate the input of a cast iron boiler with 73% efficiency and a heat loss of 122,000 btu/hr?

To calculate the input of a cast iron boiler given its efficiency and heat loss, you use the relationship that defines efficiency. Efficiency is expressed as the ratio of useful output to total input, often calculated as a percentage.

In this scenario, the efficiency of the boiler is 73%, which means that 73% of the energy input is converted into useful heat output, while the remaining 27% is lost or not utilized. Given that the heat loss is 122,000 BTU/hr, this heat loss represents the useful output that is available from the boiler. To find the total energy input required to achieve this heat output, you need to adjust for the efficiency.

The correct calculation involves dividing the heat output (heat loss in this case) by the efficiency (as a decimal). The formula to convert percentage efficiency into decimal form is to divide the percentage by 100, so 73 becomes 0.73. The correct calculation thus becomes:

Total Input = Heat Loss / Efficiency = 122,000 BTU/hr / 0.73

If you rearrange this in a more calculation-friendly format, you might express it as (122,000 BTU/hr / 73) x 100, which matches the structure of the correct