Question

On a hot day, the temperature of an 80,000-L swimming pool increases by 1.50ºC. What is the net heat transfer during this heating? Ignore any complications, such as loss of water by evaporation.

a) 1.20 × 10⁹ J
b) 2.02 × 10⁹ J
c) 1.92 × 10⁵ J
d) 1.35 × 10⁵ J

Answer 1

To calculate the net heat transfer for the heating of an 80,000-L swimming pool by 1.50°C, the formula Q = mcΔT is used, yielding a result of approximately 5.02 × 10^8 J. This result does not match the provided options, suggesting there may be an error in the choices given or the details of the question.

Step-by-step explanation:

Calculating Net Heat Transfer for a Swimming Pool

To determine the net heat transfer for an 80,000-L swimming pool with a temperature increase of 1.50°C, we can use the formula Q = mcΔT, where:

• Q is the heat transfer,
• m is the mass of the water,
• c is the specific heat capacity of water (approximately 4.186 J/g°C), and
• ΔT is the change in temperature.

First, we convert the volume of water to mass (since the density of water is about 1 g/mL, 80,000 L equals 80,000,000 g). Then, we calculate the heat using the given temperature change:

Q = (80,000,000 g)(4.186 J/g°C)(1.50°C)

After calculating, the net heat transfer Q is approximately 5.02 × 108 J (joules), which is not among the provided choices. There might be a mistake in the choices or an error in the question's details.