The melting point of a solid is 90°C. What is the heat required to change 2.5 kg of this solid at 30°C to a liquid?
The specific heat of the solid is (390 J/(kg.K)) and its heat of fusion is (4000 J/kg).
This is two problems rolled into one.
q1 = heat required to raise T of solid from 40.0 C to 90.0 C.
q1 = mass x specific heat x delta T.
q2 = heat required to melt the solid once the T has reached 90.0 C.
q2 = mass x heat of fusion.
Total heat = q1 + q2.
The melting point of a solid is 90°C. What is the heat required to change 2.5 kg of this solid at 30°C to a liquid?
The specific heat of the solid is (390 J/(kg.K)) and its heat of fusion is (4000 J/kg).
To calculate the heat required to change a solid at a certain temperature to a liquid, we need to consider two processes: heating the solid from its initial temperature to its melting point, and then melting the solid at its melting point.
First, let's calculate the heat required to raise the temperature of the solid from 30°C to its melting point of 90°C. We can use the formula Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Q1 = m * c * ΔT1
= 2.5 kg * 390 J/(kg·K) * (90°C - 30°C)
= 2.5 kg * 390 J/(kg·K) * 60°C
= 58500 J
Next, let's calculate the heat required to melt the solid at its melting point. This can be done using the formula Q = m * ΔHf, where Q is the heat, m is the mass, and ΔHf is the heat of fusion.
Q2 = m * ΔHf
= 2.5 kg * 4000 J/kg
= 10000 J
Now, we can find the total heat required by summing Q1 and Q2.
Total heat required = Q1 + Q2
= 58500 J + 10000 J
= 68500 J
Therefore, the heat required to change 2.5 kg of the solid at 30°C to a liquid is 68500 J.