Question: 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

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 radiation, the rate of which is given (approximately) by:

where k is a constant and A is the area of the radiator. Prove that, for fixed power output |Ẇ| and for fixed temperature T_H, the radiator area A is a minimum when the temperature ratio T_C / T_H is 0.75.

lcl= kAT 47 C

Step by Step Solution

★★★★★

3.33 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Introduction To Chemical Engineering Thermodynamics Questions!

Acme Corporation has been operating profitably since its creation in 1998. At the beginning of 2022, Acme acquired a 70 percent ownership in Beta Company. At the acquisition date, Acme prepared the...

A heat engine operating between 200C and 80.0C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work?

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 gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of 700C and 27.0C. (a) What is the maximum efficiency of a heat engine operating between these temperatures? (b) Find...

Answer question 4,5,6,10 4. [-/2 Points] DETAILS OBINPHYS8 5.P.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER machinist wishes to insert a copper rod with a diameter of 9 mm into a hole with a...

A Carnot heat engine operating between a high T H and low T L energy reservoirs has an efficiency given by the temperatures. Compare this to two combined heat engines, one operating between T H and...

Any part of the question complete would be helpful. I will give an amazing review, thanks!! Initials: Problem 6 - 25 points n moles of a diatomic ideal gas experience the following thermodynamic...

Chapter 14 All about Heat and Work In This Chapter Understanding the laws of thermodynamics Working with isobaric processes Handling isochoric processes Calculating isothermal processes his chapter...

We've studied the Carnot cycle in class, but in reality the Carnot cycle is not useful as it has reversible processes that are infinitesimally slow, and hence a system operating at Carnot efficiency...

1)A Carnot engine takes 3000 J from a reservoir at 600 K, does some work, and discards some heat to a reservoir at 300 K. How much work does it do? A 1500 J B 500 J C 2500 J D 300 J 2)A 700 g...

A solution of benzene (CH) and toluene (C7Hs) is 29.0 benzene by mass. At 25C the vapor pressures of pure benzene and pure toluene are 94.2 and 28.4 torr, respectively. Why is the composition of the...

Over the last few years, many state governments have reduced tax revenue through tax rate reductions and even elimination of certain taxes. At the federal government level, income tax rates continue...

Explain why a $500 million increase in government purchases of goods and services will generate a larger rise in real GDP than a $500 million increase in government transfers.

4. Produce the maximum improvement in a limited time.

Liquids (identified below) at 25C are completely vaporized at 1(atm) in a countercurrent heat exchanger. Saturated steam is the heating medium, available at four pressures: 4.5, 9, 17, and 33 bar....

Of the processes proposed in Probs. 7.50 and 7.51, which would you recommend? Why? Problem 7.50 Liquid benzene at 25C and 1.2 bar is converted to vapor at 200C and 5 bar in a twostep steady-flow...

Liquid benzene at 25C and 1.2 bar is converted to vapor at 200C and 5 bar in a two-step steady-flow process: vaporization in a counter flow heat exchanger at 1.2 bar, followed by compression as a gas...

Cumulative preferred stock: A) has a right to vote cumulatively B) requires dividends in arrears to be carried over into the next period. C) has a claim to dividends after common stock D) generally...

Happy Cleaners needs a new steam finishing machine that costs $100,000. The company is evaluating whether it should lease or purchase the machine. The equipment falls into the MACRS 3-year class, and...

\# Your company is considering 2 projects, Project IOT and Project ERP, each of which requires and initial outlay of 50 million BDT. Your company uses a financial model for project selection, BCR and...