An 8.0 g ice cube at -10^∘ C is put into a Thermos flask containing 100 cm^3 of water at 20^∘

An 8.0 g ice cube at -10^∘ C is put into a Thermos flask...

Key Concepts

Latent Heat

Latent heat is the heat absorbed or released by a substance during a phase change at constant temperature. During processes such as melting or freezing, energy is used to change the phase rather than to change the temperature, and this energy transfer must be accounted for separately in entropy calculations.

Entropy

Entropy is a thermodynamic state function that quantifies the degree of disorder or randomness in a system. It is a central concept in the second law of thermodynamics, which states that for any spontaneous process the total entropy of an isolated system will increase, reflecting the irreversibility of natural processes.

Entropy Change Calculation

Entropy change in a process can be calculated by integrating the infinitesimal amount of reversible heat transfer divided by the temperature at which the transfer occurs (?S = ?dQ_rev/T). This method is used for processes where temperature, phase, or other conditions might vary, requiring the integration over the path of the process.

Heat Transfer

Heat transfer is the process by which energy in the form of thermal energy is exchanged between systems or substances as a result of a temperature difference. In thermodynamics, analyzing heat transfer is crucial to determining how energy is redistributed within a composite system until thermal equilibrium is reached.

Specific Heat Capacity

Specific heat capacity is a material property that indicates the amount of heat required to change the temperature of a unit mass of a substance by one degree Kelvin (or Celsius) without a phase change. It plays an essential role in calculating the heat energy involved during a temperature change in a substance.

Thermal Equilibrium

Thermal equilibrium refers to the state in which all parts of a system have reached a common temperature, and no net heat flow occurs between the components. Achieving equilibrium is a key goal in many thermodynamic problems, and the process often involves several steps of heat exchange that contribute to the overall entropy change.

Transcript

00:01 So here, we know that in coming to equilibrium, the heat lost by the 100 cubic centimeters of liquid water is absorbed by the mass.

00:11 So we can say that the change in heat transfer would equal zero because we're going to say that because it is in a thermos, there isn't going to be any heat transfer between the system and its environment.

00:27 So we can say that the heat transfer from the warm water cooling plus the heat transfer from the ice warming or rather ice warms to zero degrees celsius plus the heat needed for the ice to melt plus the heat needed for the melted ice to warm.

01:05 This is all equaling zero.

01:09 So we can say that the specific heat of water times the mass of the water times temperature final minus 20 degrees plus mass of the ice specific heat of the ice times zero degrees minus negative 10 degrees plus the latent heat of formation for water times the mass of the ice plus the mass of the water times the specific heat.

01:38 Sorry, the mass of the ice times the specific heat of the water times temperature final minus zero degrees celsius.

01:50 This is equaling zero.

01:52 And essentially we're trying to find the final temperature.

01:56 We know that here the specific heat, the latent heat of formation is equaling 330 ,000 joules per kilogram and we can then solve at this point, also knowing that the specific heat of water is equaling 4 ,190 joules per kilogram per kelvin, we can then say that the final temperature is going to be equal to approximately 12 .24 degrees celsius.

02:42 Now, this is going to be equivalent to essentially 285 .39 kelvin, and this is simply adding 273 .15 kelvin to the temperature in celsius in order to convert to kelvin.

03:01 So converting to kelvin from celsius is simply adding 273 .15.

03:09 We can then use a sample problem 20 .01...

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