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Chapter 14: Problem 20

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

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

Step by step solution

01

List the given values

Mass (m) = 50.0 kg, initial temperature (T1) = 37.0掳C, final temperature (T2) = 38.4掳C, specific heat capacity (c) = 4.18 J/g掳C
02

Calculate the temperature change

螖T = T2 - T1 = 38.4掳C - 37.0掳C = 1.4掳C
03

Convert mass from kg to grams

1 kg = 1000 g, so 50.0 kg = 50.0 * 1000 = 50000 g
04

Calculate the heat (Q)

Use the formula Q = mc螖T. Plug in the values: Q = (50000 g) * (4.18 J/g掳C) * (1.4掳C) Q = 292600 J
05

Present the final answer

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

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Most popular questions from this chapter

A blacksmith heats a 0.38 -kg piece of iron to \(498^{\circ} \mathrm{C}\) in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at \(20.0^{\circ} \mathrm{C},\) what minimum amount of water must be in the bucket to cool the iron to \(23.0^{\circ} \mathrm{C} ?\) The water in the bucket should remain in the liquid phase.
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