The melting point of a solid is 90.0C. What is the heat required to change 2.5 kg of this solid at 30.0C to a liquid? The specific heat of the solid is 390 J/kgK and its heat of fusion is 4000 J/kg.
To determine the heat required to change 2.5 kg of a solid at 30.0°C to a liquid, we need to consider two factors: heating the solid from 30.0°C to its melting point and then melting the solid at the given melting point.
First, let's calculate the heat required to raise the temperature of the solid from 30.0°C to its melting point, 90.0°C. We use the formula:
Q1 = m * c * ΔT1
where:
Q1 is the heat required,
m is the mass of the solid (2.5 kg),
c is the specific heat of the solid (390 J/kgK), and
ΔT1 is the change in temperature (T_final - T_initial = 90.0°C - 30.0°C).
Plugging in the values, we get:
Q1 = 2.5 kg * 390 J/kgK * (90.0°C - 30.0°C)
Simplifying:
Q1 = 2.5 kg * 390 J/kgK * 60.0°C
Next, let's calculate the heat required to melt the solid. We use the formula:
Q2 = m * ΔH_fusion
where:
Q2 is the heat required,
m is the mass of the solid (2.5 kg), and
ΔH_fusion is the heat of fusion (4000 J/kg).
Plugging in the values, we get:
Q2 = 2.5 kg * 4000 J/kg
Now, to calculate the total heat required, we add Q1 and Q2:
Total Heat = Q1 + Q2
Substituting the calculated values:
Total Heat = (2.5 kg * 390 J/kgK * 60.0°C) + (2.5 kg * 4000 J/kg)
Finally, we can simplify and calculate the Total Heat:
Total Heat = 585,000 J + 10,000 J
Total Heat = 595,000 J
Therefore, the heat required to change 2.5 kg of this solid at 30.0°C to a liquid is 595,000 Joules.