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Chapter 17: Problem 10

Which takes more heat: melting a gram of ice already at \(0^{\circ} \mathrm{C},\) or bringing the melted water to the boiling point?

Short Answer

Expert verified
Heating the water from 0掳C to 100掳C takes more heat.

Step by step solution

01

Calculate the heat required to melt ice

The heat Q required to change the state of a substance can be calculated using Q=ml, where m is the mass and l is the latent heat. For ice, the latent heat of fusion (l) is approximately \(334 \, J/g\). So for 1 gram of ice, Q = 1g * 334 J/g = 334 J.
02

Calculate the heat needed to bring water to boiling point

The heat Q needed to increase the temperature of a substance can be found with Q=mc鈭員, where m is the mass, c is the specific heat capacity, and 鈭員 is the change in temperature. For water, c is approximately \(4.18 \, J/g掳C\). The temperature change from 0掳C to 100掳C is 100 degrees. So, Q = 1g * 4.18 J/g掳C * 100掳C = 418 J.
03

Compare the two heats

The heat needed to melt 1g of ice (334J) is compared to the heat needed to heat 1g of water from 0掳C to 100掳C (418J). It's clear that heating water takes more heat.

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