Question: A reversible heat engine operates in outer space. The only way heat can be rejected is by radiation, which is proportional to the fourth power

A reversible heat engine operates in outer space. The only way heat can be rejected is by radiation, which is proportional to the fourth power of the temperature and the area of the radiating surface. Show that for a given power output and a given source temperature (T1), the area of the radiator is minimized when the radiating surface temperature is T2 = 0.75 T1.

Step by Step Solution

★★★★★

3.54 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For the reversible e... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

861-ME-T (6931).docx

120 KBs Word File

Students Have Also Explored These Related Mechanical Engineering Questions!

Suppose the heat engine in Problem 39 is operated in reverse as a refrigerator. What is its refrigeration efficiency? Data From Problem 39 A reversible heat engine operates between thermal reservoirs...

A reversible heat engine operates between thermal reservoirs at 900 K and 200 K. If 9000 J are extracted from the hot reservoir, how much work is done by the heat engine?

A reversible heat engine operates between a hot reservoir at 580 K and a cold reservoir of unknown temperature. After 5 min, the engine has absorbed 1000 J of energy from the hot reservoir and...

Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation, which is proportional to the radiator area and the fourth power of...

Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine onl by thermal radiation, which is proportional to the radiator area and the fourth power of...

Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation, which is proportional to the radiator area and the fourth power of...

A reversible heat engine operates between temperatures of 1 0 0 0 K and 3 0 0 K . Plot the rate of heat input from the high - temperature reservoir and the heat rejected from the low temperature...

A heat engine operating in outer space may be assumed equivalent to a Carnot engine operating between reservoirs at temperatures T H and T C . The only way heat can be discarded from the engine is by...

Approximately 40 percent of the water that is pumped in the United States is used to cool power plants. Sufficient quantities of water may not be available in arid regions, necessitating use of...

Dunes called the Sauna Resort Hotel and made a reservation for his family of four for July 6-12. A letter of confirmation signed by the hotel manager stated, This is to confirm your reservation for...

At the beginning of the year, the balance in the Allowance for Doubtful Accounts is a credit of $665.During the year, $392 of previously written-off accounts were reinstated and accounts totaling...

Question 1 5 2 5 pts Application fees, tuition, and fines are all examples of prices. ( 1 0 . 0 1 2 ) True False

Find (a) f 1 t, (b) f 2 t, (c) f t, and (d) fyt and state their domains. f sxd s3 2 x , tsxd sx2 2 1

In large compressors, the gas is frequently cooled while being compressed to reduce the power consumed by the compressor. Explain how cooling the gas during a compression process reduces the power...

To control an isentropic steam turbine, a throttle valve is placed in the steam line leading to the turbine inlet. Steam at 6 MPa and 600°C is supplied to the throttle inlet, and the turbine...

Two rigid tanks are connected by a valve. Tank A is insulated and contains 0.2 m3 of steam at 400 kPa and 80 percent quality. Tank B is uninsulated and contains 3 kg of steam at 200 kPa and 250C. The...

The next dividend payment by Halestorm, Inc., will be $1.56 per share. The dividends are anticipated to maintain a growth rate of 4 percent forever. The stock currently sells for $29 per share. What...

A company has the information about the following accounting numbers: Cost of Goods Sold = $8,200, Accounts Receivable = $4,185, Inventory = $1,606, Credit Sales = $11,500, and Accounts Payable =...

PLEASE ANSWER ALL 4 MULTIPLE CHOICE QUESTIONS "Non-conventional" typically refers to projects that: Have no investment up front Have the only investment occurring up front Have a later outflow in...