Suppose that the temperature of the water in the previous problem is raised by first bringing it

Suppose that the temperature of the water in the previous...

Key Concepts

Thermal Reservoir

A thermal reservoir is an idealized body with a very large thermal capacity that can absorb or supply finite amounts of heat without undergoing a significant change in temperature. Because of this property, the reservoir's temperature remains constant during heat exchange, simplifying the calculation and interpretation of entropy changes in both the reservoir and the system it interacts with.

Second Law of Thermodynamics

The second law of thermodynamics states that in any spontaneous process the total entropy of the universe increases, guiding the direction of natural processes. This law is fundamental when evaluating the overall entropy change of a system coupled with its environment, and it underpins the analysis of whether processes such as the stepwise heating described are reversible or irreversible.

Entropy Change in Heat Transfer

Entropy change due to heat transfer is calculated by dividing the amount of heat exchanged by the absolute temperature at which the exchange occurs. This concept applies particularly cleanly in scenarios involving reservoirs, where the temperature is assumed constant, allowing for direct computation of the system’s and reservoir’s contributions to the total entropy change.

Entropy

Entropy is a thermodynamic state function that quantifies the degree of disorder or randomness in a system, as well as the distribution of energy among its particles. It is central to understanding how energy is dispersed in physical processes and is a key factor in determining the direction of spontaneous change according to the second law of thermodynamics.

Thermal Equilibrium

Thermal equilibrium refers to the state reached when two bodies in contact with each other no longer exchange heat, meaning they have attained the same temperature. In this condition, the net energy transfer between the bodies is zero, and the concepts of entropy change become particularly useful in analyzing how the system’s energy distribution aligns with the surroundings.

Transcript

00:04 So here, weight of water is given as 200 gram or say 200 multiplied by 10 to power minus 3 kilogram.

00:16 Now, t initial, temperature initial of in the first stage of water as given is 0 degree c or we can say as 273 kelvin.

00:34 Now the temperature final of first water is equal to 40 degree c is equal to 273 kelvin.

00:48 So temperature of the reservoir in the first reservoir is as first reservoir is as 40 degree c is equal to 20 degree c is equal to 2 .7.

01:05 Is equal to 313 kelvin and also here 313 kelvin.

01:22 Now then further the water is in thermal contact with the second reservoir whereas temperature of t initial with the second stage of water as given as 40 degree c is equal to 313 kelvin and temperature final of second water is given as 80 degree c equal to the second reservoir so that will be 353 kelvin so the temperature of the second reservoir or say is equal to 80 degree c and 3 3 3 53k.

02:21 So for calculation by the part a we know that delta s of the reservoir as given is q upon t because t is constant.

02:38 So we know that the heat lost by the reservoirs is gained by the water.

02:43 So water is gaining heat.

02:45 So that will be q1 will be equal to minus q water in the first stage.

02:52 So here we know hence qw1 will be equal to mwcw temperature of final of the first stage of water minus temperature initial of the first stage of water.

03:17 So delta as we can say of reservoir first will be.

03:27 Equal to the mw cw t final of first water minus t initial of first water and divided by t of reservoir first so here putting the value we get the delta s of our reservoir 1 will be equal to minus 0 .2 multiplied by 4186 multiplied by 4186 multiplied by 40 minus 0 divided by 40 plus 273 so delta s of reservoir 1 will be equal to minus 105 minus 10 it is minus 107 jule per kelvin so this is the entropy of the first reservoir wire change in this process now we will use the same procedure for the entropy change of the second reservoir the process is same temperature is again constant for the second reservoir so here delta s of reservoir will be equal to q by t now therefore the delta s of reservoir 2 will be equal to q2 upon temperature of reservoir 2...

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