An unknown mass of a certain solid, initially at
60⁰C, is heated at a uniform at a uniform rate.
After 4.0 min the solid reaches its melting point
of 80⁰C, and it remains at that temperature for
3.0 min until completely melted. After a further
6.0 min of heating, the resulting liquid is at 145C. if the specific heat of the substance in the solid state is 1.8 KJ/KgC, find:
a. latent heat of fusion of the substance
b. its specific heat in the liquid substance
Anong sagot?
To find the answers to these questions, we need to apply the principles of heat transfer and energy conservation. Let's break down the problem step by step:
Step 1: Find the heat absorbed by the solid as it is heated to the melting point.
To find the heat absorbed by the solid, we'll use the formula:
Q = mcΔT
Where:
Q is the heat absorbed
m is the mass of the solid
c is the specific heat of the solid state substance
ΔT is the change in temperature
In this case, the solid is heated from 60⁰C to 80⁰C. So, the change in temperature is:
ΔT = 80⁰C - 60⁰C = 20⁰C
Substituting the values into the formula, we have:
Q = mcΔT = m * 1.8 KJ/KgC * 20⁰C
Step 2: Find the heat absorbed during the melting process.
During the melting process, the solid remains at its melting point temperature and absorbs heat to complete the phase change from solid to liquid.
The heat absorbed during the melting process is given by:
Q = mL
Where:
Q is the heat absorbed
m is the mass of the solid
L is the latent heat of fusion
Step 3: Find the heat absorbed by the liquid as it is heated further.
To find the heat absorbed by the liquid, we'll use the same formula as in Step 1:
Q = mcΔT
In this case, the liquid is heated from its melting point (80⁰C) to 145⁰C. So, the change in temperature is:
ΔT = 145⁰C - 80⁰C = 65⁰C
Substituting the values into the formula, we have:
Q = mcΔT = m * c * ΔT
Step 4: Calculate the answers to the questions.
a. To find the latent heat of fusion (L), we can use the information given in the problem statement. We know that after heating for 4.0 min, the solid reaches its melting point and remains at that temperature for 3.0 min until completely melted.
So, the heat absorbed during the melting process is:
Q = mL = Q_during_melting = 0 (Since no change in temperature during melting)
Substituting this into the equation, we have:
0 = m * L
Therefore, L = 0.
b. To find the specific heat of the liquid substance (c), we need to calculate the heat absorbed by the liquid during the heating process, using the values obtained in Step 3.
Q = mcΔT
Substituting the values into the formula, we have:
Q = mcΔT = m * c * ΔT = 0 (Since no change in temperature during melting)
Since the heat absorbed during the heating process is zero, we can't determine the specific heat of the liquid substance from the given data.
In conclusion:
a. The latent heat of fusion (L) is 0.
b. The specific heat of the liquid substance (c) cannot be determined from the given data.