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Chapter 10: Problem 129

In regions with dry climates, evaporative coolers are used to cool air. A typical electric air conditioner is rated at \(1.00 \times 10^{4}\) Btu/h $(1 \mathrm{Btu}, \text { or British thermal unit }=\text { amount of energy to }$ raise the temperature of 1 \(\mathrm{lb}\) water by \(1^{\circ} \mathrm{F}\) ). What quantity of water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner?

Short Answer

Expert verified
The quantity of water that must be evaporated each hour to dissipate as much heat as a typical electric air conditioner is \(1.00 \times 10^{4}\) lb/h.

Step by step solution

01

Write the energy required equation

The energy required to evaporate the water is given by the formula: \(Q = m \cdot c\) Since the energy dissipated by the air conditioner is given as \(1.00 \times 10^{4}\) Btu/h, we need to equate this value to the energy required to evaporate the water: \(1.00 \times 10^{4} \text{ Btu/h} = m \cdot c\)
02

Substitute the value of specific heat

The specific heat of water is given as 1 Btu/lb°F. Substitute this value into the equation: \(1.00 \times 10^{4} \text{ Btu/h} = m \cdot 1 \text{ Btu/lb°F}\)
03

Solve for the mass of water

Now, solve the equation for \(m\), the mass of water that needs to be evaporated per hour: \(m = \frac{1.00 \times 10^{4} \text{ Btu/h}}{1 \text{ Btu/lb°F}} = 1.00 \times 10^{4} \text{ lb/h}\) The quantity of water that must be evaporated each hour to dissipate as much heat as a typical electric air conditioner is \(1.00 \times 10^{4}\) lb/h.

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