Which of the following requires the most heat to achieve? Show answer choices A Completely melting a 10 kg block of ice at 0°C. Completely boiling a 10 kg pot of water at a temperature of 100°C. C Heating a 10 kg block ot copper from 1100°C to 2100°C. B D) Heating a 10 kg block of lead from 500°C to 1500°C. E Completely boiling a 10 kg sample of mercury at a temperature of 357°C.
The question involves calculating the amount of heat required to achieve a certain change in temperature for different materials. The formula used in this type of problem is:
Q = mcΔT
where Q is the amount of heat transferred, m is the mass of the material, c is the specific heat capacity of the material, and ΔT is the change in temperature.
To completely melt a 10 kg block of ice at 0 C, we need to transfer heat to the ice to raise its temperature from 0 C to its melting point, and then supply additional heat to overcome the latent heat of fusion, which is the heat required to convert the ice to water at its melting point. The amount of heat required for this process is:
Q = m×(c_ice×ΔT + Lf)
where c_ice is the specific heat capacity of ice, Lf is the latent heat of fusion of ice, and ΔT is the change in temperature from 0 C to the melting point of ice, which is 0 C.
For completely boiling a 10 kg pot of water at a temperature of 100 C, we need to transfer heat to the water to raise its temperature from 100 C to its boiling point, and then supply additional heat to overcome the latent heat of vaporization, which is the heat required to convert the water to steam at its boiling point. The amount of heat required for this process is:
Q = m×(cwater×ΔT + Lv)
where c_water is the specific heat capacity of water, Lv is the latent heat of vaporization of water, and ΔT is the change in temperature from 100 C to the boiling point of water, which is also 100 C.
For heating a 10 kg block of copper from 1100 C to 2100 C, we need to transfer heat to the copper to raise its temperature from 1100 C to 2100 C. The amount of heat required for this process is:
Q = m×c_copper×ΔT
where c_copper is the specific heat capacity of copper, and ΔT is the change in temperature from 1100 C to 2100 C.
For heating a 10 kg block of lead from 500 C to 1500 C, we need to transfer heat to the lead to raise its temperature from 500 C to 1500 C. The amount of heat required for this process is:
Q = m×c_lead×ΔT
where c_lead is the specific heat capacity of lead, and ΔT is the change in temperature from 500 C to 1500 C.
For completely boiling a 10 kg sample of mercury at a temperature of 357 C, we need to transfer heat to the mercury to raise its temperature from 357 C to its boiling point, and then supply additional heat to overcome the latent heat of vaporization, which is the heat required to convert the mercury to vapor at its boiling point. The amount of heat required for this process is:
Q = m×(c_mercury×ΔT + Lm)
where c_mercury is the specific heat capacity of mercury, Lm is the latent heat of vaporization of mercury, and ΔT is the change in temperature from 357 C to the boiling point of mercury.
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