Question

Following vigorous exercise, the body temperature of an (80.0 , kg) person is (40.0° C). At what rate in watts must the person transfer thermal energy to reduce the body temperature to (37.0° C) in (30.0 , min), assuming the body continues to produce energy at the rate of (150 , W)?

a) (128.8 , W)
b) (212.3 , W)
c) (180.0 , W)
d) (240.5 , W)

Answer 1

The rate at which thermal energy must be transferred to reduce the body temperature of an 80.0-kg person from 40.0°C to 37.0°C in 30.0 min can be calculated using the formula: Rate of energy transfer = (change in thermal energy) / (time). Given that the person continues to produce energy at the rate of 150 W, the rate of energy transfer to reduce the body temperature is the difference between the rate of energy transfer and the rate of energy produced by the body.

Step-by-step explanation:

The rate at which thermal energy must be transferred to reduce the body temperature of an 80.0-kg person from 40.0°C to 37.0°C in 30.0 min can be calculated using the formula:

Rate of energy transfer (W) = (change in thermal energy) / (time)

The change in thermal energy can be calculated using the formula:

change in thermal energy (J) = mass (kg) x specific heat capacity (J/kg°C) x change in temperature (°C)

Given that the person continues to produce energy at the rate of 150 W, the total rate of energy transfer is the sum of the rate of energy transfer to reduce the body temperature and the rate of energy produced by the body. Therefore, the rate of energy transfer to reduce the body temperature is:

Rate of energy transfer to reduce body temperature (W) = (change in thermal energy) / (time) - rate of energy produced by the body (W)