The gravothermal catastrophe. This is a variant on a classic celestial me- chanics result. We're going...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The gravothermal catastrophe. This is a variant on a classic celestial me- chanics result. We're going to start with the result of the last problem, and with the stellar heat capacity problem from homework 2. We start out with a star with mass M and size R. For the moment, let's say it's made up of hydrogen. (a) What is the temperature of the star, T? (b) We surround the star with a cloud of ideal gas (stars are born in clouds of ideal gas) of hydrogen. For simplicity, we assume that it has the same mass as the star. Its temperature Tg is lower than that of the star. Draw a plot of entropy vs. energy for both the star and the gas. (c) With this assumption about the mass and content of the two systems, what is the relationship between the heat capacity of the gas and the heat capacity of the star? (d) Let a tiny amount of heat, AU flow from one system to the other. What are the temperatures T and T of the star and gas after this amount of energy transfers? Which way does heat flow? Hints: use the heat capacities to relate AU to temperatures. Let the second law guide you! (e) Imagine that heat keeps flowing from one part of your system to the other. Do you reach thermal equilibrium? If so, at what temperature? (f) you have a relationship between the energy of a star, its size, and its temperature. How does the radius of the star change with the energy and temperature of the star, as the system evolves? The gravothermal catastrophe. This is a variant on a classic celestial me- chanics result. We're going to start with the result of the last problem, and with the stellar heat capacity problem from homework 2. We start out with a star with mass M and size R. For the moment, let's say it's made up of hydrogen. (a) What is the temperature of the star, T? (b) We surround the star with a cloud of ideal gas (stars are born in clouds of ideal gas) of hydrogen. For simplicity, we assume that it has the same mass as the star. Its temperature Tg is lower than that of the star. Draw a plot of entropy vs. energy for both the star and the gas. (c) With this assumption about the mass and content of the two systems, what is the relationship between the heat capacity of the gas and the heat capacity of the star? (d) Let a tiny amount of heat, AU flow from one system to the other. What are the temperatures T and T of the star and gas after this amount of energy transfers? Which way does heat flow? Hints: use the heat capacities to relate AU to temperatures. Let the second law guide you! (e) Imagine that heat keeps flowing from one part of your system to the other. Do you reach thermal equilibrium? If so, at what temperature? (f) you have a relationship between the energy of a star, its size, and its temperature. How does the radius of the star change with the energy and temperature of the star, as the system evolves?
Expert Answer:
Answer rating: 100% (QA)
ANSWER a The temperature of the star T can be found by equating the gravitational potential energy of the star to its thermal energy The gravitational potential energy of a spherical object of mass M ... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
If you were going to start a home-based business consulting in a dorm room what do you think would be the greatest challenge you faced? What about if you were starting the same business from home?
-
Let's imagine that you were going to start a company that produces spectroscopes to sell to general chemistry students. How could you ensure that all the spectroscopes created the same calibration...
-
If you were going to start a corporation and expected to need to raise capital from several investors, would you include preferred stock in your capital structure? Why or why not? If your answer is...
-
print_list Favorite Language/Type: Author: Write a function named print_list that accepts a list of integers as a parameter and prints them, one per line, in the format shown. Your code should work...
-
Refer to Problem 18.4. Sergeant Desk believes the failures are related to reading ability. She regresses whether these same 400 troops failed (Y) on their reading test scores (X, scored in terms of...
-
Consider the following program: Boolean blocked [2]; Int turn; Void P (int id) { While (true) { Blocked [id] = true; While (turn! = id) { While (blocked [1-id]) /* do nothing */; Turn = id; } /*...
-
Explain the overall patterns of production strategies and their relationship to the environment.
-
AAA Lock Manufacturing Co. makes and sells several models of locks. The cost records for the ZForce lock show that manufacturing costs total $29.00 per lock. An analysis of this amount indicates that...
-
1. Give your thoughts on the article. Good, bad, indifferent? 2. What are some 'out of the box' ideas to update capitalism? Read this article:...
-
There is an array A made of N integers. Your task is to choose as many integers from A as possible so that, when they are put in ascending order, all of the differences between all pairs of...
-
In early January 2022, Ben was talking with her sister and business partner Jinkx regarding the preliminary income statements for DeLaItes Dress Boutique for 2021 (See Exhibit 1 ). Since January 1,...
-
The globalization of markets refers to moving away from thinking a. the market for your product is local. b. that other countries are interested in trade. c. that every component of a product must be...
-
Think of an example of how a specific organization (for-profit or not-for-profit) tried to establish a better customer relationship with you. What did the organization do? Was it effective? Why or...
-
Phishing can be used to a. minimize the taxes owed to the federal government. b. steal identity information from unsuspecting clients. c. record the keystrokes typed in when someone is logging into a...
-
Societal marketing began after the Great Depression when the economy was improving and most of society wanted to spend. True or False
-
Employees can benefit from successful marketing because new job opportunities may be created as production expands to satisfy the growing demand for highly valued products. True or False
-
Every packet has 4 addresses, the source and destination IP address and the source and destination MAC address. Which address does a router use to determine which port to send the data out of?...
-
Classify each of the following activities as proper or prohibited under the various consumer statutes you have studied. a. Calling a hospital room to talk to a debtor who is a patient there. b....
-
How would you go about finding a lawyer for your business?
-
What sorts of primary data could you collect using observation for your carwash?
-
Ahmad has two sources of capital for his business equity at a cost of 15% and debt at a cost of 10%. Figure his weighted average cost of capital at 75/25 equity/debt, 50/50 equity debt, and 30/70...
-
FIFO and average cost flow methods periodic and perpetual inventory systems Non-GST version Clean Air Ltd sells air purifiers. The table below summarises the inventory movements for the most popular...
-
Personal Tech Ltd records its inventory of fitness watches using the FIFO cost allocation for perpetual inventory. The following information summarises the inventory movements for their most popular...
-
Audio Attitude Ltd uses the perpetual inventory system to maintain its inventory records of Play it car stereos. The computerised accounting system identified the closing inventory value was \($245\)...
Study smarter with the SolutionInn App