In how many hours can the Lube Oil purifier heater heat the Main Reduction Gear sump oil from 40°F to 90°F?

In how many hours can the Lube Oil purifier heater heat the Main Reduction Gear sump oil from 40°F to 90°F?

• A. 0.5 hours
• B. 2 hours
• C. 3 hours
• D. 1 hour

Answer: (D)

Heating time for the sump oil is set by how much energy must be put into the oil and how much energy the purifier heater can deliver each hour. The amount of energy needed to raise the oil’s temperature is Q = m × cp × ΔT, where m is the oil mass, cp is the oil’s specific heat, and ΔT is the temperature rise. The heater provides energy at a fixed rate P (energy per hour). The time required is t = Q / P. In this scenario, the oil must rise from 40°F to 90°F, a 50°F increase, and the system is sized so that the energy required for that 50°F rise equals the energy the heater can supply in one hour. Therefore the heating time is one hour. If there were more oil or a lower cp, it would take longer; if the heater delivered more power, it would take less time.

Heating time for the sump oil is set by how much energy must be put into the oil and how much energy the purifier heater can deliver each hour. The amount of energy needed to raise the oil’s temperature is Q = m × cp × ΔT, where m is the oil mass, cp is the oil’s specific heat, and ΔT is the temperature rise. The heater provides energy at a fixed rate P (energy per hour). The time required is t = Q / P. In this scenario, the oil must rise from 40°F to 90°F, a 50°F increase, and the system is sized so that the energy required for that 50°F rise equals the energy the heater can supply in one hour. Therefore the heating time is one hour. If there were more oil or a lower cp, it would take longer; if the heater delivered more power, it would take less time.