A 75-hp (shaft output) motor that has an efficiency of 91.0 percent is worn out and is replaced by a high-efficiency 75-hp motor that has an efficiency of 95.7 percent. Determine the reduction in the heat gain of the room due to higher efficiency under full-load conditions.

reduction in heat will be 3.525 hp (or 52.22% reduction relative to the initial heat gain)

Step-by-step explanation:

for the first since 91 % of power input is converted to work, then the remaining 100-91=9% is dissipated as heat to the room

then for the new motor, 100-95.7=4.3% of power input is dissipated as heat

the reduction in heat will be

ΔQ=75 hp * (9%-4.3%) = 3.525 hp

or

ΔQ/Q initial = 75 hp * (9%-4.3%) / (75 hp*9%) = 1-4.3%/9% = 52.22%