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Chapter 9: Q18. (page 342)

In Exercises 17-20, the latitude of a city is given. Sketch the earth and a circle of latitude through the city. Find the radius of this circle.

Columbus, Obie; 40°N

Short Answer

Expert verified

(a)

The final answer is 4902.68km.

Step by step solution

01

Step 1. Given information:

The latitude of a city Columbus, Ohio is 43°N.

02

Step 2. Concept used:

We use basic geometric and angle concept

03

Step 3. Applying the concept:

Sketch of earth:

Now, from the figure, r=Rcos43°, where Ris the radius of the earth, and ris a radius of required circle.

∴   r=6400×cos43,∘

⇒   r=4680.66 km.

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Most popular questions from this chapter

Given: PT¯is tangent to ⊙Oat T;TS¯⊥PO¯

Complete the following statements.

a. TS is the geometric mean between ? and ?

b. TO is the geometric mean between ? and ?

c. If OS=6 and SP=24,TS=? and TP=?

For each exercise draw ⊙O with radius 12. Then draw radii OA¯ and to OB¯ form an angle with the measure named. Find the length of AB¯.

c.m∠AOB=60°

To get more than an infinitesimal amount of work out of a Carnot engine, we would have to keep the temperature of its working substance below that of the hot reservoir and above that of the cold reservoir by non-infinitesimal amounts. Consider, then, a Carnot cycle in which the working substance is at temperature \(T_{h w}\) as it absorbs heat from the hot reservoir, and at temperature Thwas it expels heat to the cold reservoir. Under most circumstances the rates of heat transfer will be directly proportional to the temperature differences:

QhΔt=KTh−ThwandQcΔt=KTcw−Tc

I've assumed here for simplicity that the constants of proportionality (K)are the same for both of these processes. Let us also assume that both processes take the

same amount of time, so the Δt′sare the same in both of these equations.

(a) Assuming that no new entropy is created during the cycle except during the two heat transfer processes, derive an equation that relates the four temperatures Th,Tc,Thw,andTcw

(b) Assuming that the time required for the two adiabatic steps is negligible, write down an expression for the power (work per unit time) output of this engine. Use the first and second laws to write the power entirely in terms of the four temperatures (and the constant (K)), then eliminate Tcwusing the result of part (a).

(c) When the cost of building an engine is much greater than the cost of fuel (as is often the case), it is desirable to optimize the engine for maximum power output, not maximum efficiency. Show that, for fixed ThandTc, the expression you found in part (b) has a maximum value at Thw=12Th+ThTc. (Hint: You'll have to solve a quadratic equation.) Find the corresponding expression for TCW

(d) Show that the efficiency of this engine is 1−Tc/Th. Evaluate this efficiency numerically for a typical coal-fired steam turbine with Th=600∘CTc=25∘C, and compare to the ideal Carnot efficiency for this temperature range. Which value is closer to the actual efficiency, about 40%, of a real coal-burning power plant?

Given PA¯and PB¯ are tangents to ⊙o.

Use the diagram at the right to explain how the corollary on page 333

follows from Theorem9-1.

PA¯, PB¯,and RS¯ are tangents.

Explain, Why PR+RS+SP=PA+PB.
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