The melting point of a solid is 90.0 degrees C. What is the heat required to change 2.5 of this solid at 40.0 degrees C to a liquid? The specific heat of the solid is 390 J/kg (K) and its heat of fusion is 4000 J/kg.
A. 4.9 10^4 J
B. 1.0 10^4 J
C. 5.9 10^4 J
D. 5.0 10^4 J
I am leaning towards C, but I need help understanding the process a bit more thoroughly. Thanks!
I assume that the amount to be melted is 2.5 kg. If you start out at the melting point (40 C), the energy reguired is 4000 J/kg x 2.5 kg = ?
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To determine the heat required to change a solid at a certain temperature to a liquid, you need to consider two factors: the heat required to raise the temperature of the solid from its initial temperature to its melting point, and the heat required to melt the solid at its melting point.
Let's break down the problem step by step:
Step 1: Calculate the heat required to raise the temperature of the solid from 40.0 degrees C to its melting point of 90.0 degrees C.
The formula to calculate the heat transfer (Q) is:
Q = m * c * ∆T
Where:
Q = heat transfer (in joules)
m = mass of the solid (in kilograms)
c = specific heat of the solid (in joules per kilogram per degree Celsius)
∆T = change in temperature (in degrees Celsius)
In this case, m = 2.5 kg, c = 390 J/kg (K), and ∆T = (90.0 - 40.0) = 50.0 degrees C.
Now, plug these values into the formula:
Q1 = 2.5 kg * 390 J/kg (K) * 50.0 degrees C
Q1 = 48750 J
So, the heat required to raise the temperature of the solid is 48750 J.
Step 2: Calculate the heat required to melt the solid.
The formula to calculate the heat transfer during a phase change (such as melting) is:
Q = m * L
Where:
Q = heat transfer (in joules)
m = mass of the solid (in kilograms)
L = heat of fusion (in joules per kilogram)
In this case, m = 2.5 kg and L = 4000 J/kg.
Now, plug these values into the formula:
Q2 = 2.5 kg * 4000 J/kg
Q2 = 10000 J
So, the heat required to melt the solid is 10000 J.
Step 3: Calculate the total heat required.
To calculate the total heat required, you need to add the heat required to raise the temperature (Q1) and the heat required to melt the solid (Q2).
Total Q = Q1 + Q2 = 48750 J + 10000 J = 58750 J
Therefore, the total heat required to change 2.5 kg of the solid at 40.0 degrees C to a liquid is 58750 J.
Looking at the answer choices, we find that option C (5.9 * 10^4 J) is the closest match to the calculated value.
So, the correct answer is C.
Yes kg.
So the answer is B?