Question

How much heat is required to raise the body temperature of a \(50.0-\mathrm{kg}\) woman from \(37.0^{\circ} \mathrm{C}\) to $38.4^{\circ} \mathrm{C} ?$

Short answer

Question: Calculate the heat required to raise the body temperature of a 50.0 kg woman from 37.0°C to 38.4°C. Assume the specific heat capacity of the human body is approximately the same as that of water (4.18 J/g°C). Answer: The heat required to raise the body temperature of a 50.0 kg woman from 37.0°C to 38.4°C is 292,600 J.

Step-by-step solution

List the given values

Mass (m) = 50.0 kg, initial temperature (T1) = 37.0°C, final temperature (T2) = 38.4°C, specific heat capacity (c) = 4.18 J/g°C

Calculate the temperature change

ΔT = T2 - T1 = 38.4°C - 37.0°C = 1.4°C

Convert mass from kg to grams

1 kg = 1000 g, so 50.0 kg = 50.0 * 1000 = 50000 g

Calculate the heat (Q)

Use the formula Q = mcΔT. Plug in the values: Q = (50000 g) * (4.18 J/g°C) * (1.4°C) Q = 292600 J

Present the final answer

The heat required to raise the body temperature of a 50.0 kg woman from 37.0°C to 38.4°C is 292,600 J.