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Chapter 14: Problem 13

It is a damp, chilly day in a New England seacoast town suffering from a power failure. To warm up the cold, clammy sheets, Jen decides to fill hot water bottles to tuck between the sheets at the foot of the beds. If she wishes to heat \(2.0 \mathrm{L}\) of water on the wood stove from $20.0^{\circ} \mathrm{C}\( to \)80.0^{\circ} \mathrm{C},$ how much heat must flow into the water?

Short Answer

Expert verified
Answer: 501.6 J

Step by step solution

01

Convert volume to mass

To convert the volume of water (2.0 L) to mass, we can use the density of water. The density of water is 1 g/cm³ which is equal to 1000 kg/m³. Now, convert the volume of water (2.0 L) to mass (m) by multiplying the volume with the density of water: m = 2.0 L * 1000 kg/m³ m = 2.0 kg
02

Calculate the change in temperature

Find the change in temperature (ΔT) by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial ΔT = 80.0°C - 20.0°C ΔT = 60.0°C
03

Calculate the heat required

Now use the formula for heat transfer, Q = mcΔT, to calculate the heat required: Q = mcΔT Q = (2.0 kg) * (4.18 J/g°C) * (60.0°C) Q = 501.6 J The heat that must flow into the water to heat it from 20.0°C to 80.0°C is 501.6 J.

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