·Heat loss during breathing. In very cold weather, a...

$\cdot$ Heat loss during breathing. 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. (a) On a cold winter day when the temperature is $-20^{\circ} \mathrm{C},$ what is the amount of heat needed to warm to internal body temperature $\left(37^{\circ} \mathrm{C}\right)$ the 0.50 $\mathrm{L}$ of air exchanged with each breath? Assume that the specific heat capacity of 1.3 $\mathrm{g}$ is 1020 $\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K})$ and that 1.0 $\mathrm{L}$ of air has a mass of 1.3 $\mathrm{g}$ . (b) How much heat is lost per hour if the respiration rate is 20 breaths per minute?

Key Concepts

Rate of Energy Loss Calculation

This concept involves determining the total energy loss over a period by combining the energy required per breath with the breathing rate (breaths per minute) and converting it to an hourly rate. It illustrates how a seemingly small energy exchange per breath can accumulate to a significant total loss over time.

Heat Transfer Equation

The heat transfer equation, Q = m × c × ?T, is used to calculate the energy required to raise the temperature of a substance. In this context, it is applied to determine the energy needed to warm each breath of air from the cold outdoor temperature to the body's temperature.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is essential in calculating the heat needed to warm the air from the external temperature to the body’s internal temperature.

Mass-Volume Conversion Using Density

This concept involves converting the volume of air inhaled into mass by using the density of air. This conversion is necessary because the specific heat capacity is applied to mass, not volume.

Temperature Change (Delta T) in Heating

The temperature difference between the initial cold temperature and the body’s internal temperature determines the energy required for heating. It is a key factor in the heat transfer equation, where the energy required depends directly on this temperature change.

Transcript

00:01 All right, guys, let's take a look at the question.

00:03 Well, for the first question, we was asking us how much heat was required if we need to heat out the cold air from negative 20 degrees celsius to our body temperature, which is 37 degrees celsius.

00:16 Okay? so, while we know, the equation for the required heat is q equal to mc times delta t.

00:25 M is the mass.

00:26 C is the specific heat.

00:28 Dada t is the changing temperature.

00:30 Okay.

00:32 So we know initial temperature is negative 20 degrees celsius.

00:35 If we convert it to kelvin, it's 253 kelvin.

00:42 Okay.

00:45 And the final temperature is our human body temperature, which is 37 degrees celsius.

00:53 And we convert it to kelvin.

00:56 It's 310 kelvin.

01:00 Okay.

01:02 And so now we know the change temperature is, is equal to delta t which is t2 minus t1 which is 310 kelvin minus 153 kelvin which will give us 57 kelvin okay so that's the changing temperature in kelvin and also the specific heat for such air is given as well it was 1020 jou over kilogram times kelvin okay that's a specific heat for 1 liter error or 1 .3 grand error.

01:50 But in this case, we're talking about 0 .5 liter air in the process.

01:57 So the mass here is equal to 1 .3 grand, divided by 2, which is 0 .65 grand.

02:08 For the mass of the air, we need to raise the temperature from.

02:14 Okay, so now we have c, we have m, and we have delta t.

02:21 So q is equal to m, which is 0 .65 gram...

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