A 1 cm thick piece of lead with a surface area of 160 cm2 is placed on the surface of Mercury for 1 hour during the time the planet receives its peak solar energy. Assume the lead absorbs all of the solar energy, and its temperature when placed is at absolute zero. Will the energy received raise the temperature of the lead to its melting point of 327°C? If so, determine the mass of lead that melts. (Assume Lf of lead is 5 cal/g.)
The mass of lead melts, if the energy received raise the temperature of the lead to its melting point of
Answer to Problem 8PEB
Solution:
Explanation of Solution
Given data:
A
The energy received raise temperature of the lead to its melting pon of
Latent heat of lead is
Formula used:
Write the expression of density.
Here,
Write the formula for heat:
Here,
Write the equation for latent heat
Here,
Explanation:
According to the question volume of lead is as follows:
Recall the expression of density to find the mass of lead.
Substitute
Determine the energy required to heat the lead to its melting point:
Mass of lead is
Specific heat of mercury is
Initial temperature is
Final temperature is
Recall the formula for heat:
Substitute
Refer the table 15.1 to the value of mercury of solar energy received.
Convert time to seconds:
Determine the energy received, use solar energy received multiply it by the area and the duration of the time.
Substitute
Compare the energy received to the energy required to heat the lead and its melting point:
Therefore, the lead will reach its melting point.
Determine the excess energy:
Substitute
Recall the equation for latent heat
Substitute
Conclusion:
The mass of lead melts are
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