At noon on a clear day in midsummer, a cylindrical titanium plate... 51. At noon

Question

At noon on a clear day in midsummer, a cylindrical titanium plate...

51. At noon on a clear day in midsummer, a cylindrical titanium plate is placed in the sun. The plate is painted flat black so that it will absorb most of the energy from the sunlight rather than reflecting it. The plate is 5 centimeters [cm] in diameter, one centimeter [cm] thick, has a specific gravity of 4.5, a molecular weight of 47.9 grams per mole Ig/mol] and has a specific heat capacity of 25 joules per mole kelvin [ J/ (mol K)]. If the temperature of the plate increased by 17 degrees Fahrenheit [°F], how much energy in units of calories [cal] did it absorb from the sun, assuming no heat is reradiated to the surroundings?

Explanation / Answer

Volume of plate = (pi*52/4)*1 = 19.635 cm3 = 19.635*10-6 m3

Specific gravity = 4.5

Density of titanium = 4500kg/m3

mass of titanium plate = 4500*19.635*10-6 =0.08836 kg = 88.36 gm

Number of moles of titanium present =88.36/47.9=1.84 moles

speicific heat capacity = 25 Joules per mole kelvin

Increase in temperature = 17 degrees Fahrenheit = 17/1.8=9.44 degrees Celcius = 9.44 Kelvin

Energy absorbed by plate = 1.84*25*9.44=434.24 Joules = 434.24/4.18=103.9 Calories

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