What change in entropy occurs when a 27.9-g ice cube at -12^∘ C is transformed into steam at 115

What change in entropy occurs when a 27.9-g ice cube at...

Key Concepts

Entropy

Entropy is a thermodynamic state function that measures the disorder or randomness in a system. It quantifies the number of specific ways in which a system may be arranged, often interpreted as the unavailability of a system’s energy to do work. Changes in entropy are calculated by considering the heat exchanged at different temperatures during a process.

Phase Transitions

Phase transitions involve changes in the state of matter, such as melting (solid to liquid) and vaporization (liquid to gas), where energy is absorbed or released without a change in temperature. These processes require the addition or removal of latent heat, and the associated entropy change is determined by dividing the latent heat by the constant transition temperature.

Heat Transfer and Specific Heat Capacity

Heating or cooling a substance involves transferring energy to or from it, which changes the temperature according to the substance’s specific heat capacity. The entropy change during such temperature changes is calculated by integrating the reversible heat transfer (dQ) over the temperature (T), highlighting the contribution of temperature-dependent energy changes.

Latent Heat

Latent heat is the amount of energy absorbed or released by a substance during a phase change at constant temperature. It is used in calculating the entropy change during phase transitions by using the formula ?S = Q/T, where Q is the latent heat and T is the temperature during the phase change.

Transcript

00:01 We can calculate the change in entropy of a reversible process as d s equal to dq by t where t is the constant temperature and dq is the heat absorbed if the system's temperature is not a constant then we can calculate the change in entropy as an integral integral initial to final states dq by t so here we have 27 .9 grams of ice at minus 12 degrees celsius and it is changing to steam at 115 degrees celsius so we have two kinds of processes are here and we can use d is equal to dq by t where dq is the heat absorbed so as ice changes to water and water changes to steam we have two processes at constant temperature where we can use delta as equal to dq which is the heat absorbed at that constant temperature process that is mass into latent heats of vaporization and latent heat of melting.

01:15 So these can be used at that places and for the changes involving temperature we can use delta as equals initial to final states in that place that is when ice change.

01:32 To water at 0 degrees celsius then water changes to water at 0 degrees celsius changes to water at 100 degrees celsius and steam at 100 degrees celsius changes to steam at 115 degrees celsius we can use that places in bowls change in temperature so it is the heat absorbed there is m into c c's a specific heat into t t or change in temperature by t this can be used and this can be simplified as m into c into integral d t by t that is log t final by t initial so we have two formulas here and we can use these first let us change you calculate the change in entropy when ice at minus 12 degrees celsius to i set zero degrees celsius that is delta s 1 so here we can we have to use the specific heat of ice and the temperatures must be in kelvin scale so minus 12 degrees celsius equal to 261 kelvin and zero degree celsius equal to 273 kelvin so here delta s1 equal to mass m c i's into log 273 by 261 that is equal to masses in grams we have to convert it into kilogram 0 .0027 into c is 2090 into log 273 by 261 into log 27 by 261 that is equal to 2 .54 jule per kelvin.

03:41 Now the next change taking place here is ice is melting.

03:49 So ice melt delta s2 equal to m.

03:58 L by t.

04:00 L is the latent heat of ice or latent heat of melting.

04:04 That is equal to 0 .0027 into latent heat here.

04:10 Is 3 .33 into 10 raised to 5 divided by the constant temperature which is 273 kelvin that is equal to 32 .9 jule per kelvin and next we have water at 0 degrees celsius and it acts of heat and changes its temperature to 100 degrees celsius that is equal to m c water into log 100 degrees celsius is 373 divided by 273.

04:49 So that is equal to 0 .027 into 4186, which is the specific heat of water into log 273 divided by, no, 373 divided by 273 divided by 273...

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