Final answer:
To calculate the amount of heat energy needed to change 10 kg of water at 50 °C to steam at 120 °C, you need to consider the heat energy required for temperature change and heat energy required for vaporization. Use the formula q = mcΔT to calculate the heat energy for temperature change, and multiply the mass of the water by the heat of vaporization to calculate the heat energy for vaporization. Add these two values together to find the total heat energy needed.
Step-by-step explanation:
To determine the amount of heat energy needed to change 10 kg of water at 50 °C to steam at 120 °C, we need to consider the various steps involved in this process.
First, we need to calculate the heat energy needed to raise the temperature of the water from 50 °C to its boiling point, which is 100 °C. We can use the formula:
Heat energy = mass × specific heat capacity × temperature change
Using the specific heat capacity of water as 4.184 J/g °C and the mass as 10,000 g (since 1 kg = 1000 g), the temperature change is (100 - 50) °C. Plugging these values into the formula, we get:
Heat energy = 10,000 g × 4.184 J/g °C × (100 - 50) °C
Once the water reaches its boiling point, we need to calculate the heat energy required to convert it into steam. This is known as the heat of vaporization. The heat of vaporization for water is approximately 2260 J/g. So, the heat energy needed to change 10 kg of water to steam is:
Heat energy = mass × heat of vaporization
Plugging in the mass as 10,000 g, we get:
Heat energy = 10,000 g × 2260 J/g
Finally, we add the heat energy required for the temperature change and the heat energy required for vaporization to get the total heat energy needed:
Total heat energy = heat energy for temperature change + heat energy for vaporization
Q_total = Q_sensible + Q_latent
= 293040 J + 22600000 J
= 22893040 J
Therefore, the total heat energy required is approximately 2.3 x 10⁷ J.
So the answer is c) 2.3 x 10⁷ J.