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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 17, Problem 26a

In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. On a cold winter day when the temperature is -20°C, what amount of heat is needed to warm to body temperature (37°C) the 0.50 L of air exchanged with each breath? Assume that the specific heat of air is 1020 J/kg K and that 1.0 L of air has mass 1.3 × 10-3 kg.

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First, identify the initial and final temperatures of the air. The initial temperature is -20°C, and the final temperature is 37°C. Convert these temperatures to Kelvin by adding 273.15 to each.
Calculate the change in temperature (ΔT) by subtracting the initial temperature from the final temperature in Kelvin.
Determine the mass of the air exchanged with each breath. Given that 1.0 L of air has a mass of 1.3 * 10^-3 kg, calculate the mass for 0.50 L of air by multiplying the volume by the mass per liter.
Use the formula for heat transfer: Q = mcΔT, where Q is the heat energy, m is the mass of the air, c is the specific heat capacity of air (1020 J/kg K), and ΔT is the change in temperature. Substitute the values you have calculated into this formula.
Solve the equation to find the amount of heat needed to warm the air from -20°C to 37°C. This will give you the energy expended in warming the air per breath.

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Key Concepts

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

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is crucial for calculating the heat needed to warm air from -20°C to 37°C. In this problem, the specific heat of air is given as 1020 J/kg K, which helps determine the energy required for temperature change.
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Mass of Air

The mass of air is essential for calculating the total heat required to change its temperature. Given that 1.0 L of air has a mass of 1.3 * 10^-3 kg, we can find the mass of 0.50 L of air by multiplying this value by 0.50. This mass, combined with the specific heat capacity, allows us to compute the heat needed for warming the air.
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Temperature Change

Temperature change is the difference between the initial and final temperatures of the air. In this scenario, the air is warmed from -20°C to 37°C, resulting in a temperature change of 57°C. This change is used in conjunction with the specific heat capacity and mass of air to calculate the total heat required using the formula Q = mcΔT.
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Related Practice
Textbook Question

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