You find a large sheet of gold, that weighs 1 kg and is 1 cm thick sitting in yo

Question

You find a large sheet of gold, that weighs 1 kg and is 1 cm thick sitting in your backyard. You want to pick it up, but it's been sitting in the sun for the past hour and it may be too hot to handle. Calculate the temperature of the gold. The room temperature heat capacity of gold is 128 J/kg K. At noon, the sun is illuminating 100 mW/cm" of energy. Assume that the gold docs not lose any heat to the surrounding environment (i.e., that it's adiabatic... this is probably not a great assumption, but it will give you an estimate of the maximum possible temperature of the gold).

Explanation / Answer

Heat capacity of the gold =128 J/KgK

weight of gold sheet=1 Kg

density of the gold=19.3g/cm3

so area of the gold sheet=51.8134 cm2

but the sun is illuminating an energy of 100 mW/cm2

so energy falling on the plate per second = 100*10-6*51.8134=5.18134*10-3J

energy fallen on the plate for 1 hr=5.18134*10-3*3600=18.653 J

we are assuming that no energy is given out

so mcp(T)=total energy fallen on tthe plate

maximum possible change in the temperature would be 0.14572 kelvin

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