(II) Suppose that three main-sequence stars could undergo the ...

Question

(II) Suppose that three main-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H–R diagram of Fig. 44–35. For each case, describe the changes in temperature, intrinsic luminosity, and size.

Accepted Answer

Welcome back everyone in a lab simulation of stellar evolution. Scientists study the behavior of three glowing gas spheres that represent stellar analogs on a diagram similar to the Hertzsprung Russell diagram. These gas spheres undergo specific transitions represented by arrows, XY and Z on the diagram for arrow X, the gas sphere moves horizontally to the left arrow Y, the gas sphere moves vertically downward and arrow Z the gas sphere moves horizontally to the right. The scientists observe changes in the gas spheres surface temperatures, energy output or luminosity and physical size during each transition. And our task is to figure out what those changes are here. We have a diagram or sorry or HR diagram showing our gas directions. And for our answer choices, A says that for A X, the temperature increases, luminosity stays the same and size decreases. B sorry. It says for A Y we're still on answer choice. A for A Y, the temperature stays the same, the luminosity decreases and the size decreases. And for RZ the temperature decreases, luminosity stays the same and size increases. Answer choice B says that for X, the temperature increases, luminosity increases and the size decreases for Y, the temperature luminosity and the size decrease and for Z, the temperature decreases, the luminosity stays the same and the size increases. In answer choice C for X, the temperature stays the same while the luminosity increases and the size decreases in ry, the temperature and luminosity decrease. While the size increases. And for Z, the temperature increases, the luminosity stays the same and the size decreases. And in answer choice D it says the temperature and luminosity decrease and the size increases Y, the temperature and luminosity increase and the size decreases. And for Z, the temperature decreases while the luminosity and the size increases. Now we can figure out OK, what happens to the sphere is the gas spheres surface temperature energy output and physical size by using our diagram. OK. And when we look at the axis of our diagram, it's gonna help us to figure out what's happening. So for example, let's take arrow X, OK. Let's take arrow X. Now for A X where our gas sphere moves horizontally to the left for our surface temperature. Since the gas sphere moves to the left on the diagram, it corresponds to an increasing temperature which we can notice here because hotter stars are on the left of the HR diagram. So for A X, the temperature increases, temperature increases. And next, if we are talking about the luminosity, since the movement is horizontal, there is no change in luminosity as luminosity changes corresponds to vertical movements. So our luminosity stays the same. And finally, OK. For our size, using the Stefan Boltzmann law for constant luminosity, an increase in temperature means that the radius must decrease. Therefore, the size decreases. OK. So we notice how helpful our diagram is for us, let's do the same for arrows Y and Z. OK. Now, for Roy, where the gas sphere moves vertically downward, the movement is vertical. So there's not gonna be any change in temperature. So the temperature temperature remains the same or the temperature stays the same. OK. I know for the luminosity since the gas moves downward, it corresponds to a decrease in luminosity. So our luminosity decreases. Yeah, luminosity decreases. And now since temperature remains constant, the decrease in luminosity implies that the radius must decrease as luminosity depends on both the radius and temperature. So thus, we can say that the size also decreases. Finally, let's look at Roz. Now, in this case, the gas sphere moves horizontally to the right. Remember that cooler stars are on the right of the Hr diagram. So that means then that for the gas sphere to move to the right, it corresponds to a decreasing temperature. In this case, the temperature decreases. When we talk about the luminosity. Since the movement is horizontal, there is no change in luminosity as luminosity changes corresponds to vertical movements. So that tells us then that the luminosity stays the same. Finally, for our size by the Stefan Boltzmann law for constant luminosity, a decrease in temperature must mean the our decrease in temperature means the radius must increase. So thus, this tells us then that the size of our gas increases. So this gives us an overview of what happens for our gasses for arrows, Xy and Z. And now when we compare them to our answer choices, OK, we can see that answer. Choice. A is the correct answer. Thanks for watching everyone. I hope this video helped.

(II) Suppose that three main-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H–R diagram of Fig. 44–35. For each case, describe the changes in temperature, intrinsic luminosity, and size.

Key Concepts

Hertzsprung-Russell (H–R) Diagram

Stellar Evolution

Intrinsic Luminosity

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