Objects A and B have the same mass of 4.3 kg and are at their melting points. They melt when 4.9 × 104 J of heat is added to A and when 12 × 104 J is added to B. (a), (b) Determine the latent heat of fusion for the substance from which each object is made. (c) Find the heat required to melt object A when its mass is 8.6 kg.
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(A) melting point of a = 4.9*10^4 J mass of a = 4.3 kg
melting point of a / mass of a = 11395.35 J/kg
(B) melting point of b = 12*10^4 J mass of b = 4.3 kg
melting point of b / mass of b = 27906.97 J/kg [WileyPlus answer would also be 2.8E4 J/kg]
(C) latent heat of fusion from A * mass of A
(11395.35 J/kg) * 8.6 kg = 98000.01 J
To find the latent heat of fusion for the substance from which objects A and B are made, we need to use the equation:
Q = mL
where Q is the heat added, m is the mass of the substance, and L is the latent heat of fusion.
(a) To find the latent heat of fusion for object A, we'll use the given information:
Q(A) = 4.9 × 10⁴ J
m(A) = 4.3 kg
Substituting these values into the equation, we get:
4.9 × 10⁴ J = 4.3 kg × L(A)
Now solve for L(A):
L(A) = (4.9 × 10⁴ J)/(4.3 kg)
= 1.14 × 10⁴ J/kg
Therefore, the latent heat of fusion for the substance from which object A is made is 1.14 × 10⁴ J/kg.
(b) To find the latent heat of fusion for object B, we'll use the given information:
Q(B) = 12 × 10⁴ J
m(B) = 4.3 kg
Substituting these values into the equation, we get:
12 × 10⁴ J = 4.3 kg × L(B)
Now solve for L(B):
L(B) = (12 × 10⁴ J)/(4.3 kg)
= 2.79 × 10⁴ J/kg
Therefore, the latent heat of fusion for the substance from which object B is made is 2.79 × 10⁴ J/kg.
(c) To find the heat required to melt object A when its mass is 8.6 kg, we'll use the equation:
Q = mL
Substituting the values into the equation, we get:
Q = 8.6 kg × L(A)
= 8.6 kg × (1.14 × 10⁴ J/kg)
= 9.804 × 10⁴ J
Therefore, the heat required to melt object A when its mass is 8.6 kg is 9.804 × 10⁴ J.
To find the latent heat of fusion for the substance from which each object is made, we can use the formula:
Latent heat of fusion = Heat added / Mass
(a) For object A:
Mass = 4.3 kg
Heat added = 4.9 × 10^4 J
Latent heat of fusion for object A = (4.9 × 10^4 J) / (4.3 kg)
To find the numerical value, we can substitute the values into the formula:
Latent heat of fusion for object A = 1.14 × 10^4 J/kg
(b) For object B:
Mass = 4.3 kg
Heat added = 12 × 10^4 J
Latent heat of fusion for object B = (12 × 10^4 J) / (4.3 kg)
To find the numerical value, we can substitute the values into the formula:
Latent heat of fusion for object B = 2.79 × 10^4 J/kg
(c) To find the heat required to melt object A when its mass is 8.6 kg, we can use the concept of proportionality:
Heat required A (when mass = 8.6 kg) / Heat required A (when mass = 4.3 kg) = Mass A (when mass = 8.6 kg) / Mass A (when mass = 4.3 kg)
Plugging in the values we know:
Heat required A (when mass = 8.6 kg) / (4.9 × 10^4 J) = 8.6 kg / 4.3 kg
Now, we can calculate the heat required:
Heat required A (when mass = 8.6 kg) = (8.6 kg / 4.3 kg) × (4.9 × 10^4 J)
Heat required A (when mass = 8.6 kg) = 2 × (4.9 × 10^4 J)
Simplifying the calculation further:
Heat required A (when mass = 8.6 kg) = 9.8 × 10^4 J
Therefore, the heat required to melt object A when its mass is 8.6 kg is 9.8 × 10^4 J.
I hope this explanation helps! If you have any further questions, feel free to ask.
latent heat of fusion is the heat required to melt a substance
the heat absorbed by a substance at it's melting point
... no temperature change ... a phase change from solid to liquid
usually given in ... Joules per gram ... heat / mass
for (c) ... more mass needs more heat to melt ... direct proportion