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Heat Problem Set: Heat Capacity of Water

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1. The air temperature above coastal areas is profoundly influenced by the large specific heat capacity of water. How large of a volume of air can be cooled by 1.0 C if energy is transferred as heat from the air to the water, thus increasing the temperature of 1.0 kg of water by 1.0 C? The specific heat capacity of air is approximately 1000.0 J/kg *C, and the density of air is approximately 1.29 kg/m^3.

2. Liquid nitrogen, which has a boiling point of 77 K, is commonly used to cool substances to low temperatures. How much energy must be removed from 1.0 kg of gaseous nitrogen at 77 K for it to completely liquefy?

3. How much energy is needed to melt exactly 1000 aluminum cans, each with a mass of 14.0 g, for recycling? Assume an initial temperature of 26.4 C.

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Solution Preview

The heat lost by air will be equal to the heat absorbed by water.
We have, heat lost or absorbed,

q = m*c*dT

where m is the mass, c is the specific heat capacity and dT is the change in temperature (final temp-initial temp)

Here the change in temperature is 1C for both air and ...

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