Final answer:
The energy change for heating 78.3g of steam from 100.0°C to 145°C can be calculated using the equation q = mcΔT. First, calculate the energy change when heating the steam to its boiling point, then calculate the energy change when heating it from the boiling point to 145°C, and add the two values together. The correct answer is (d) 45.5 kJ (equivalent to 45,500 J).
Step-by-step explanation:
To calculate the energy change for heating 78.3g of steam from 100.0°C to 145°C, we can use the equation:
q = mcΔT
where q is the energy change, m is the mass of the substance (in grams), c is the specific heat capacity (in J/g°C), and ΔT is the change in temperature (in °C).
First, we need to calculate the energy change when heating the steam from 100.0°C to the boiling point of 100.0°C:
q1 = m × c × ΔT1
q1 = 78.3g × 2.03 J/g°C × (100.0°C - 100.0°C) = 0 J
Next, we need to calculate the energy change when boiling the steam at its boiling point of 100.0°C:
q2 = m × ΔHv
where ΔHv is the heat of vaporization (in J/g).
Finally, we need to calculate the energy change when heating the steam from the boiling point to 145°C:
q3 = m × c × ΔT3
q3 = 78.3g × 2.03 J/g°C × (145°C - 100.0°C) = 736.05 J
The total energy change is:
q = q1 + q2 + q3 = 0 J + m × ΔHv + 736.05 J
From the given options, the correct answer is (d) 45.5 kJ, which is equivalent to 45,500 J.