Ch. 19 - Heat and the First Law of Thermodynamics

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

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Giancoli Douglas 5th edition

Ch. 19 - Heat and the First Law of Thermodynamics

Problem 104b

Chapter 19, Problem 104b

Metabolizing 1.0 kg of fat results in about 3.7 x 10⁷ J of internal energy in the body. How long would it take to burn 1.0 kg of fat this way assuming there is no food intake?

Verified step by step guidance

Identify the energy required to metabolize 1.0 kg of fat, which is given as 3.7 × 10⁷ J. This represents the total energy that needs to be burned.

Determine the rate at which energy is burned by the body. This is typically given as the basal metabolic rate (BMR) or energy expenditure rate. If not provided, you may need to use an average value for a human, such as 100 W (1 W = 1 J/s).

Use the formula for time:

t = \frac{E}{P}

, where

E

is the total energy (3.7 × 10⁷ J) and

P

is the power or energy expenditure rate (e.g., 100 W).

Substitute the values into the formula:

t = \frac{3.7 × 10⁷}{100}

. Ensure the units are consistent (J for energy and W for power, where 1 W = 1 J/s).

Simplify the expression to find the time

t

in seconds. If needed, convert the result into hours by dividing by 3600 (since 1 hour = 3600 seconds).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another. In this context, the body converts the chemical energy stored in fat into internal energy, which is essential for maintaining bodily functions. Understanding this concept is crucial for calculating how long it takes to utilize a specific amount of energy.

Metabolic Rate

Metabolic rate is the rate at which the body expends energy or burns calories to maintain basic physiological functions. It varies based on factors such as age, sex, and activity level. Knowing the metabolic rate is vital for determining how long it would take to burn a certain amount of energy, such as that derived from 1.0 kg of fat.

Energy Balance

Energy balance is the relationship between energy intake and energy expenditure. When energy intake is less than energy expenditure, the body uses stored energy, such as fat, to meet its needs. This concept is important for understanding the implications of burning fat without food intake, as it directly affects how long it will take to metabolize the stored energy.

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Related Practice

Textbook Question

A leaf of area 40cm² and mass 4.5 x 10⁻⁴ kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kgK. Estimate the energy absorbed per second by the leaf from the Sun.

Textbook Question

A 12-g lead bullet traveling at 220 m/s passes through a thin wall and emerges at a speed of 160 m/s. If the bullet absorbs 50% of the heat generated, If the bullet’s initial temperature was 20°C, will any of the bullet melt, and if so, how much?

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Textbook Question

Calculate what will happen when 1000 J of heat is added to 100 grams of water at 100°C.

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