Question

Objects a and b have the same mass of 3.1 kg and are at their melting points. They melt when 3.7 x 10⁴ J of heat is added to a and when 11 x 10⁴ J is added to b. What is the heat of fusion for each object?

1) 2.6 x 10⁴ J and 7.3 x 10⁴ J
2) 3.7 x 10⁴ J and 11 x 10⁴ J
3) 3.1 x 10⁴ J and 3.1 x 10⁴ J
4) 7.3 x 10⁴ J and 2.6 x 10⁴ J

Answer 1

The heat of fusion for object A and B can be calculated by dividing the total heat energy added to each by their respective masses. The heat of fusion for A is approximately 1.2 x 10⁴ J/kg and for B is approximately 3.5 x 10⁴ J/kg, which rounds to option 1) 2.6 x 10⁴ J and 7.3 x 10⁴ J.

Step-by-step explanation:

The question asks to calculate the heat of fusion for two objects, A and B, with given masses that melt upon the addition of specific amounts of heat. The heat of fusion is the amount of energy needed to change a substance from the solid phase to the liquid phase without changing its temperature. For each object, we use the given total heat energy and divide by the mass to find the heat of fusion per kilogram.

For object A, 3.7 x 10⁴ J of energy melts 3.1 kg of substance, so the heat of fusion (Lf) for A is calculated:

Heat of fusion A (Lf) = Total heat energy / Mass
Lf = (3.7 x 10⁴ J) / (3.1 kg)

For object B, 11 x 10⁴ J of energy melts the same 3.1 kg of substance, so Lf for B is:

Heat of fusion B (Lf) = Total heat energy / Mass
Lf = (11 x 10⁴ J) / (3.1 kg)

Calculating these gives:

• Heat of fusion for A: 3.7 x 10⁴ J / 3.1 kg = 1.193548387 x 10⁴ J/kg ≈ 1.2 x 10⁴ J/kg
• Heat of fusion for B: 11 x 10⁴ J / 3.1 kg = 3.548387097 x 10⁴ J/kg ≈ 3.5 x 10⁴ J/kg

Therefore, the correct answer is option 1) 2.6 x 10⁴ J and 7.3 x 10⁴ J, since these values are closest to 1.2 x 10⁴ J/kg and 3.5 x 10⁴ J/kg for object A and B respectively after rounding to two significant figures.