### Estimating Electrical Energy Required to Maintain Waterbed TemperatureMost people find waterbeds uncomfortable unless the water temperature is maintained at about 85 °F. In this example, a waterbed with a capacity of 622 liters of water cools from 85 °F to 61 °F over 24 hours without heating. We will estimate the amount of electrical energy required, measured in kilowatt-hours (kWh), to keep the waterbed from cooling.#### Given Data:- **Specific heat of water**: 4.184 J/(g·°C)- **Initial temperature (T₁)**: 85 °F- **Final temperature (T₂)**: 61 °F- **Volume of water**: 622 L- **1 kilowatt-hour (kWh)** = 3.6 × 10⁶ J- **Density of water**: 1.0 g/mL (independent of temperature)#### Steps to Calculate Electrical Energy Required:1. **Convert Temperatures from Fahrenheit to Celsius**: - $ T₁ (\text{in °C}) = \frac{(T₁ - 32)}{1.8} $ - $ T₂ (\text{in °C}) = \frac{(T₂ - 32)}{1.8} $2. **Calculate the temperature change (ΔT)**: - $ \Delta T (\text{in °C}) = T₁ - T₂ $3. **Convert Volume of Water to Mass**: - 1 liter (L) = 1000 grams (g) - Mass (m) = Volume (V) × Density (ρ)4. **Calculate Energy Required Using Specific Heat Formula**: - $ Q (\text{in J}) = m × c × ΔT $5. **Convert Energy from Joules (J) to Kilowatt-Hours (kWh)**: - $ \text{Energy (in kWh)} = \frac{Q}{3.6 × 10^6} $By following these steps, you will be able to estimate the energy required to keep the waterbed at a comfortable temperature over 24 hours.

Volume = 622L Initial temperature = 85°F Final temperature = 61°F Specific heat of water = 4.184…

Most people find waterbeds uncomfortable unless the water (specific heat of 4.184 J/g °C) temperature is maintained at about 85 °F. Unless it is heated, a waterbed that contains 622 L of water cools from 85 °F to 61 °F in 24 hours. Estimate the amount of electrical energy required over 24 hours, in kWh, to keep the bed from cooling. Note that 1 kilowatt-hour (kWh) = 3.6 x 106 J, and assume that the density of water is 1.0 g/mL (independent of temperature).

Most people find waterbeds uncomfortable unless the water (specific heat of 4.184 J/g °C) temperature is maintained at about 85 °F. Unless it is heated, a waterbed that contains 622 L of water cools from 85 °F to 61 °F in 24 hours. Estimate the amount of electrical energy required over 24 hours, in kWh, to keep the bed from cooling. Note that 1 kilowatt-hour (kWh) = 3.6 x 106 J, and assume that the density of water is 1.0 g/mL (independent of temperature).

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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