A power station boiler produces some steam. The steam loses 5.65 x 10^9 J of thermal energy when it is condensed into water. The specific latent heat of vaporisation of water is 2.... A power station boiler produces some steam. The steam loses 5.65 x 10^9 J of thermal energy when it is condensed into water. The specific latent heat of vaporisation of water is 2.26 x 10^6 J kg^-1. Calculate the mass of steam converted into water by the cooling tower. Show your working.
Understand the Problem
The question is asking to calculate the mass of steam that is converted into water when it loses a specified amount of thermal energy, using the given specific latent heat of vaporisation. The process involves applying the formula that connects thermal energy, mass, and latent heat.
Answer
The mass of steam converted into water is approximately \( 2500 \, \text{kg} \).
Answer for screen readers
The mass of steam converted into water is approximately ( 2500 , \text{kg} ).
Steps to Solve
- Identify the formula for mass calculation
To find the mass of steam that has condensed into water, we use the formula relating thermal energy, mass, and specific latent heat of vaporization: $$ Q = m \cdot L $$ where:
- ( Q ) is the thermal energy lost (in joules),
- ( m ) is the mass (in kg),
- ( L ) is the specific latent heat of vaporization (in J kg(^{-1})).
- Rearrange the formula to solve for mass
We rearrange the formula to isolate ( m ): $$ m = \frac{Q}{L} $$
- Substitute the known values
We substitute the values into the equation:
- Given ( Q = 5.65 \times 10^9 , \text{J} )
- Given ( L = 2.26 \times 10^6 , \text{J kg}^{-1} )
Now, plug them into the rearranged formula: $$ m = \frac{5.65 \times 10^9 , \text{J}}{2.26 \times 10^6 , \text{J kg}^{-1}} $$
- Perform the calculation
Calculate the value of ( m ): [ m \approx \frac{5.65 \times 10^9}{2.26 \times 10^6} \approx 2500 , \text{kg} ]
The mass of steam converted into water is approximately ( 2500 , \text{kg} ).
More Information
This calculation shows how much steam is converted into water based on the thermal energy it loses during the condensation process. The significant mass indicates efficient energy transfer in the cooling system of the power station.
Tips
- Forgetting to convert units, though it's not applicable here since both values are given in compatible units.
- Misplacing the decimal or calculating with incorrect exponents when performing the division.
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