The graph below shows the variation in temperature for 0.46 kg of a solid substance transitioning to a gas as energy is added to it. Of all the energy added, 1kJ was lost to the surroundings. What is the latent heat of fusion for this substance in [math: kJ/kg] ?

Question

BlackTom AI · Accepted Answer

Latent heat relates energy used for a phase change to mass: L = Q / m. The flat (constant-temperature) section of the graph at 30°C is the melting (fusion) plateau, so the energy added over that plateau equals the heat used to melt the solid (after accounting for losses).

Step-by-step reasoning and intermediate calculations:
1. Read the graph: the melting plateau extends from Energy Added = 1.0 × 10^3 J to 3.0 × 10^3 J. So the energy supplied during melting (from the heater) is
   Q_supplied = (3.0 − 1.0) × 10^3 J = 2.0 × 10^3 J.

2. Account for losses: the problem states that of all the energy added, 1.0 kJ (1000 J) was lost to the surroundings. That loss reduces the energy available to cause the phase change, so the net heat used for fusion is
   Q_net = Q_supplied − Q_lost = 2000 J − 1000 J = 1000 J.

3. Use the latent heat formula with the given mass m = 0.46 kg:
   L = Q_net / m = 1000 J / 0.46 kg = 2173.913... J/kg.

4. Convert to kJ/kg:
   L ≈ 2.174 kJ/kg ≈ 2.2 kJ/kg (to two significant figures consistent with the data).

Why this answer is correct:
- The plateau at constant temperature indicates energy goes into changing phase (latent heat) not into raising temperature. Subtracting the stated 1 kJ loss gives the actual energy that produced melting. Dividing that energy by the mass yields the latent heat per kilogram.

Why the other options are incorrect:
- a) 6.5 kJ/kg would require Q_net ≈ 0.46×6500 ≈ 2990 J, far larger than the available net 1000 J.
- b) 4.3 kJ/kg corresponds to Q_net ≈ 0.46×4300 ≈ 1978 J, roughly double the net energy after the stated loss.
- d) 8.7 kJ/kg corresponds to Q_net ≈ 0.46×8700 ≈ 4002 J, impossible given the plateau energy range and the 1 kJ loss.

Conclusion: The calculated latent heat of fusion is approximately 2.2 kJ/kg, confirming option c.

The graph below shows the variation in temperature for 0.46 kg of a solid substance transitioning to a gas as energy is added to it. Of all the energy added, 1kJ was lost to the surroundings. What is the latent heat of fusion for this substance in [math: kJ/kg] ?Single choice

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