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Show your work to get full credit, and if you need more points, i will add them if the answer you gave is right. A 3.7 kg block of copper at a temperature of 78 degree C is dropped into a bucket containing a mixture of ice and water whose total mass is 1.2 kg. When thermal equilibrium is reached the temperature of the water is 8 degree C. Now much ice was in the bucket before the copper block was placed in it? (Neglect the heat capacity of the bucket.) kg A concrete highway is built of slabs 17m long (at 23 degree C). How wide should the expansion cracks be (at 23degree C) between the slabs to prevent buckling if the annual extreme temperatures arc -35 degree C and 50 degree C?(the coefficient of linear expansion of concrete is 12 times l0'C) meters A lead bullet initially at 24.6 degree C melts just upon striking a target. Assuming that all of the initial kinetic energy of the bullet goes into the internal energy of the bullet to raise its temperature and melt it, calculate the speed of the bullet upon impact. l m/s A well-insulated styrofoani bucket contains 147 g of ice at 0 degree C. If 21 g of steam at 100 degree C is injected into the bucket, what is the final equilibrium temperature of the system?(cwatcr=4186 J/kg.degree C, Lf=33.Sxl04 j/kg, Lv=22.6xl05 J/kg) degree C When the temperature of a coin is raised by 80 degree C, the coin's diameter increases by 2.5 x l0-2 m. If the original diameter is 1.8 times 10*2 m, find the coefficient of linear expansion. (degree c)-1l

Explanation / Answer

1)

let there be x kg of ice

Heat lost by copper = heat gained by water + ice

0.39*3.7*(78-8) = x*334 + 1.2*8*4.187

so by solving this

x = 0.182 kg

so before melting there was 0.182 kg of ice in the bucket

2) maximum temperature it can go = 50 degrees

expanded length = initial length (1 + temperature difference* coefficient of expansion)

so expanded length = 17(1+((50-23)*12*10^-6)) = 17.005508 m

so width of expansion of cracks = 17.005508 - 17 m = 0.005508 m

3)

letmass of mead bullet be m

melting temperature of lead = 327.5 degrees

heat energy required to melt the bullet = m*Specific heat*(327.5-24.6) + m*latent heat of fusion

= m*0.13*302.9 + m*23 kJ = 62.377m kJ

this energy came from kinetic energy

so 0.5*m*v^2 = m*62.377*1000 J

so v = 353.2 m/s

4)let final temperature be t

heat lost by steam = heat gained by ice

21*10^-3 *22.6*10^5 + (100-t)(0.021)(4186) = 0.147*33.5*10^4 + 0.147*t*4186

47460 + 8790.6 - 87.906t = 49245 + 615.342t

so t = 9.96 degrees centegrade

so final tempereture = 9.96 degrees centegrade

5)

length difference= initial length (temperature difference* coefficient of expansion)

so 2.5*10^-5 = 1.8*10^-2 (80*coefficient of liner expansion)

so coeffiecient of linear expansion = 1.736*10^-5 (/degree centegrade)

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