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Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as 2 years.) Suppose you wish to install the extra insulation in the preceding problem. If energy cost $ 1.00 per million joules and the insulation was $4.00 per square meter, then calculate the simple payback time. Take the average Δ T for the 120-day heating season to be 15.0 ° C .

We found in the preceding problem that P = 126 Δ T W · ° C as baseline energy use. So the total heat loss during this period is Q = ( 126 J/s · ° C ) ( 15.0 ° C ) ( 120 days ) ( 86.4 × 10 3 s/day ) = 1960 × 10 6 J . At the cost of $1/MJ, the cost is $1960. From an earlier problem, the savings is 12% or $235/y. We need 150 m 2 of insulation in the attic. At $ 4 / m 2 , this is a $500 cost. So the payback period is $ 600 / ( $ 235 / y ) = 2.6 years (excluding labor costs).

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Additional problems

In 1701, the Danish astronomer Ole Rømer proposed a temperature scale with two fixed points, freezing water at 7.5 degrees, and boiling water at 60.0 degrees. What is the boiling point of oxygen, 90.2 K, on the Rømer scale?

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What is the percent error of thinking the melting point of tungsten is 3695 ° C instead of the correct value of 3695 K?

7.39 %

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An engineer wants to design a structure in which the difference in length between a steel beam and an aluminum beam remains at 0.500 m regardless of temperature, for ordinary temperatures. What must the lengths of the beams be?

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How much stress is created in a steel beam if its temperature changes from –15 ° C to 40 ° C but it cannot expand? For steel, the Young’s modulus Y = 210 × 10 9 N/m 2 from Stress, Strain, and Elastic Modulus . (Ignore the change in area resulting from the expansion.)

F A = ( 210 × 10 9 Pa ) ( 12 × 10 −6 / ° C ) ( 40 ° C ( −15 ° C ) ) = 1.4 × 10 8 N/m 2 .

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A brass rod ( Y = 90 × 10 9 N/m 2 ) , with a diameter of 0.800 cm and a length of 1.20 m when the temperature is 25 ° C , is fixed at both ends. At what temperature is the force in it at 36,000 N?

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A mercury thermometer still in use for meteorology has a bulb with a volume of 0.780 cm 3 and a tube for the mercury to expand into of inside diameter 0.130 mm. (a) Neglecting the thermal expansion of the glass, what is the spacing between marks 1 ° C apart? (b) If the thermometer is made of ordinary glass (not a good idea), what is the spacing?

a. 1.06 cm; b. 1.11 cm

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Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails ( 1 watt = 1 joule/second or 1 W = 1 J/s and
1 MW = 1 megawatt ) . (a) Calculate the rate of temperature increase in degrees Celsius per second ( ° C/s ) if the mass of the reactor core is 1.60 × 10 5 kg and it has an average specific heat of 0.3349 kJ/kg · ° C . (b) How long would it take to obtain a temperature increase of 2000 ° C , which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than that calculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the 500,000-kg steel containment vessel would also begin to heat up.)

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Questions & Answers

calculate ideal gas pressure of 0.300mol,v=2L T=40°c
Viola Reply
what is principle of superposition
Jyoti Reply
what are questions that are likely to come out during exam
King Reply
what is electricity
Jyoti Reply
watt is electricity.
electricity ka full definition with formula
If a point charge is released from rest in a uniform electric field will it follow a field line? Will it do so if the electric field is not uniform?
Sadaqat Reply
Maxwell's stress tensor is
Ami Reply
neither vector nor scalar
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Under which topic
what is electrostatics
Yakub Reply
Study of charges which are at rest
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
Practice Key Terms 9

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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