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°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.

Video transcript

Welcome back everybody. We are taking a look at the thermal regulation of a room. We are told that the volume of this room is 15, L. We are told that it is at starting out at a temperature of 5°C. Now we wish to raise this temperature up to 18°C and it's it's just normal air in here. Right, So some statistics about air, we just have that the specific heat of air is 1020 jewels per kilogram kelvin And that we have the mass for one liter of air is 1.3 times 10 to the negative third kg. And we are asked to find how much heat is needed in order to go from this temperature to this temperature. Well, we actually have a formula for that. Uh The heat needed is mass of the air times the specific heat times the change in temperature. And we have all of this. So let's just go ahead and plug it in to find the mass of air. We just multiply the mass per one liter of beer, one liter of air, sorry, times the volume. So we will have 15,400 times 1.3 times 10 to the negative third times the specific heat of air, which is 1020 Times the difference in temperature which is 13° which is equal to 265,000 jewels or 265 pillow jewels corresponding to our answer. Choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.