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Chapter 6: Problem 126

A swimming pool, 10.0 \(\mathrm{m}\) by \(4.0 \mathrm{m},\) is filled with water to a depth of 3.0 \(\mathrm{m}\) at a temperature of \(20.2^{\circ} \mathrm{C}\) . How much energy is required to raise the temperature of the water to \(24.6^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The energy required to raise the temperature of the water in the swimming pool from 20.2°C to 24.6°C is approximately 2,210,732,800 joules.

Step by step solution

01

Calculate the volume of water in the pool#

The volume V of the pool can be calculated using the formula V = length × width × height. Using the given dimensions of the pool (10.0 m × 4.0 m × 3.0 m), V = 10.0 m * 4.0 m * 3.0 m = 120.0 m³
02

Calculate the mass of the water in the pool#

To find the mass of the water, we need to multiply the volume of the water by the density of water (approximately 1,000 kg/m³): m = V × density_water = 120.0 m³ × 1,000 kg/m³ = 120,000 kg
03

Calculate the change in temperature#

ΔT is the difference between the final temperature and the initial temperature in Celsius or Kelvin: ΔT = T_final - T_initial = 24.6°C - 20.2°C = 4.4°C (or 4.4 K)
04

Calculate the energy required using the specific heat formula#

Now, we plug in the values for mass, specific heat capacity, and change in temperature into the specific heat formula: Q = mcΔT = 120,000 kg * 4,184 J/(kg·K) * 4.4 K = 2,210,732,800 J The energy required to raise the temperature of the water in the pool from 20.2°C to 24.6°C is approximately 2,210,732,800 joules.

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