 Okay, we're now going to work an example problem involving radiation. So what I'll do is I will begin by writing out the problem statement. This is a very simplified radiation example. We're going to use the equation that we derived at the end of the last segment where we consider the object to be a gray surface. Okay, so what we have, we have an astronaut sitting and working in the service bay of a spacecraft. And we're told that the astronaut is surrounded by walls at a minus 100 degrees Celsius. And area of the space suit of the astronaut is three square meters, emissivity is 0.05. And we're asked to calculate her rate of heat loss when the suit's outer temperature is zero degrees C. So she would obviously be at a warmer temperature and then there's conduction going through the suit. But the outer temperature of the suit is at zero degrees Celsius. And we're trying to calculate the amount of heat loss from the space suit. So let's write out what we know and what we're trying to find and then we'll work this problem. Okay, so we're trying to find the heat transfer from the astronaut. We're going to call that Q and it will be watts that we'll calculate because we know the area of the astronaut's space suit. So let's begin with a schematic of what is going on in this problem. Okay, so there we have the astronaut in her space suit out in space. We have vacuum conditions, so there is no mechanism of convection going on. The only form of heat transfer is going to be radiative heat transfer. And given that the astronaut's outer suit temperature is at a higher temperature than the surroundings, we know that the heat transfer, the radiative heat transfer is going to be going in that direction. So let's make a few assumptions in order to solve this problem. Steady state, so the spacecraft is not going around the earth and going from a shaded region to a region where we have solar radiation, it's operating in steady state. Second thing is we will assume this to be a gray body and with that we can then say that the absorptivity is equal to the emissivity epsilon, alpha is equal to epsilon. And so with that for analysis what we can do is we can use the equation that we came up with in the last segment. So let's begin by writing out that equation. Okay, so we have this equation, we can put in all the values. Now the one thing you got to be really careful with, I've already told you about this, is watch the temperatures whenever you have radiation because notice we have this raised to the power of four and everything else we're doing, conduction and convection. We do not have temperature raised to a power. And so it's usually a temperature differential, a temperature difference. But here we're raising temperature to the power and consequently we need the temperature to be in Kelvin or things will go awry for us very quickly. So let's plug in the values into this equation. We have the emissivity 0.05, the area of her space suit we were told was three meters squared. The Stefan-Boltzmann constant, you're going to memorize this throughout this course because you're going to use it so many times. And then finally the temperature and it has to be in Kelvin. So the first one is the surface temperature of her suit. And let me put in the Kelvin there, I'll put in the units. So that's raised to the power four. And then the surrounding temperature we're told is minus 100 so that is 173 Kelvin. Also raised to the power four. Plugging in the values we find that the heat loss from her suit is 39.6 watts. So what does that mean? Well let's do a little bit of a conversion here. Let's figure out how much food she needs to eat in order to maintain that level of heat loss. And so if we look, one calorie, a dietary calorie is 4186.8 joules. So what I'm going to do, I'm going to convert the heat loss into calories. And we're going to convert this instead of calories per second. We'll do calories per hour because that's a little bit more of a meaningful number. That's dietetic so that is relating to food. And with this we find that the heat loss translates into 34 calories per hour. And I did some looking up of values to figure out what type of food would replenish her in maintaining her temperature. And there are different things. If she wanted to eat butter, she could eat one teaspoon of butter that has 35 calories but I don't think she wants to eat butter. If she has seedless raisins, I looked it up and 22 seedless raisins have 34 calories. So if this astronaut wants to maintain the overall balance and overcoming the heat loss she would need to eat 22 raisins within an hour. So that's about a raisin every two minutes. So anyways, that gives you an idea of how to apply a radiative heat transfer. We simplify things drastically by assuming it to be a gray body. So emissivity and absorptivity are related as well. We didn't look at many of the other aspects where things are really a function of wavelength. And so radiative heat transfer can get quite complex. We're going to keep it quite simple in this course. So we're mainly going to focus on conduction and convection. So those are the three forms of heat transfer. And what we'll do in the next lecture is we're going to take a look at combining the three together into a specific problem. But that'll be in the next lecture that we are doing that. So anyways, that is radiative heat transfer.