Question

On a certain dry sunny day, a swimming pool’s temperature would rise by 1.50°C if not for evaporation. What fraction of the water must evaporate to carry away precisely enough energy to keep the temperature constant?

a) 1/3
b) 1/2
c) 2/3
d) 3/4

Answer 1

To keep the temperature constant, the fraction of water that must evaporate is 1/2.

Step-by-step explanation:

To keep the temperature constant, the energy carried away by evaporation must be equal to the energy gained due to the rise in temperature.

The energy required to raise the temperature of water can be calculated using the formula: Q = mcΔT, where Q is the energy transfer, m is the mass of water, c is the specific heat of water, and ΔT is the change in temperature.

Since the temperature rises by 1.50°C, the energy gained by the pool is Q = mcΔT = m × 1.50 × c.

On the other hand, the energy carried away by evaporation can be calculated using the latent heat of vaporization.

Let's assume the fraction of water that needs to evaporate is f.

Therefore, the energy carried away by evaporation is Q = f × mL, where L is the latent heat of vaporization.

Setting these two equations equal to each other, we can solve for the fraction of water that needs to evaporate: f = (1.50 × c) / L.

Given that c is the specific heat capacity of water and L is the latent heat of vaporization, the correct answer is f = 1/2 or option b.