Problem 1.5. The relatively unique properties of water are among the reasons why it plays such a key role in the Earth's climate. Among those properties are the ones that relate energy and water processes. Provide all answers in standard SI units. a) Define the differences (in meaning) of the heat capacity of a substance and latent heat (i.e. of vaporization or fusion) of substance. Which one is used in the context of evaporation to convert between a mass flux density and an energy flux density? What are the typical values of these properties for water at 0°C? b) What is the nominal density of liquid water? What is the nominal density of ice? Which is bigger? c) Suppose you have a 2 cm x 2 cm x 2 cm ice cube that is frozen at a temperature of 0°C. How much energy input would be required to melt it?
Problem 1.5. The relatively unique properties of water are among the reasons why it plays such a key role in the Earth's climate. Among those properties are the ones that relate energy and water processes. Provide all answers in standard SI units. a) Define the differences (in meaning) of the heat capacity of a substance and latent heat (i.e. of vaporization or fusion) of substance. Which one is used in the context of evaporation to convert between a mass flux density and an energy flux density? What are the typical values of these properties for water at 0°C? b) What is the nominal density of liquid water? What is the nominal density of ice? Which is bigger? c) Suppose you have a 2 cm x 2 cm x 2 cm ice cube that is frozen at a temperature of 0°C. How much energy input would be required to melt it?
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Transcribed Image Text:Problem 1.5. The relatively unique properties of water are
among the reasons why it plays such a key role in the Earth's
climate. Among those properties are the ones that relate
energy and water processes. Provide all answers in standard
SI units.
a) Define the differences (in meaning) of the heat capacity of
a substance and latent heat (i.e. of vaporization or fusion) of a
substance. Which one is used in the context of evaporation to
convert between a mass flux density and an energy flux
density? What are the typical values of these properties for
water at 0°C?
b) What is the nominal density of liquid water? What is the
nominal density of ice? Which is bigger?
c) Suppose you have a 2 cm x 2 cm x 2 cm ice cube that is
frozen a temperature of 0°C. How much energy input
would be required to melt it?
d) Suppose you are making yourself 0.50 liters of tea but its
temperature is 75°C, which is too hot for you to drink. In
order to cool its temperature, you immerse three ice cubes of
Transcribed Image Text:the same dimension as the one in part c) in your tea. If the
energy used to melt the ice came from the internal energy (i.e.
temperature) of the tea, what is the lowered temperature of
your tea?
e) Suppose you do not drink the all of the tea, and you leave
50 ml in the cup. How much energy would be required to fully
evaporate the remaining tea? If this energy came from the air
in a room surrounding the cup of tea, how would the air
temperature change, i.e. by what amount and as an increase
or decrease? Assume the room has dimensions of 5 m x 5 m x
3 m and the air average density is 1.2 kg/m³.
Expert Solution
Step 1
Since we answer up to three subparts, we will answer the first three. Please resubmit the question and specify the other subparts you would like to get answered.
(a) Heat capacity is a physical property of substance, it is the heat required to increase the temperature by a unit degree. The SI unit of heat capacity is .
Latent heat is the energy released or absorbed by substance during change in its phase without the change in temperature.
When the water evaporates, it converts to vapor, there is a phase change from liquid to gas, this is due to latent heat of vaporization.
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