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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

two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
Tijani Reply
what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Why does water cool when put in the pot ?
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
types of thermometer?
yemisi Reply
thermometer, Radiation thermometer and vapour pressure thermometer.liquid thermometer use thermometric liquid like mercury ,alcohol etc.
liqid thermometer ,gas thermometer, resitance thermometer,thermo electric thermometer , radiation thermometer andvapour pressure thermometer
calculate the quantity of heat required to rise the temperature of 1gmail of ice _10 to 110
Dargu Reply
A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
A wave is a periodic disturbance which travel with a finite velocity and remains unchanged in type as it travels.
What's a wave motion?
What is charge bodies
Oje Reply
which have free elections
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Charge bodies are those which have free electons
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
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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