Let an isolated system be composed of one part at T1 and second part at T2, with T2>T1. Let the parts be separated by a wall that allows heat flow at only an infinitesimal rate. Show that, when heat dq flows irreversibily from T, to T1, we have entropy change as follow: bp bp ds T1 Hint: Use two heat reservoirs to carry out the change of state reversibly. (which is positive) T2

Let an isolated system be composed of one part at T1 and second part at T2, with T2>T1. Let the parts be separated by a wall that allows heat flow at only an infinitesimal rate. Show that, when heat dq flows irreversibily from T, to T1, we have entropy change as follow: bp bp ds T1 Hint: Use two heat reservoirs to carry out the change of state reversibly. (which is positive) T2

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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4) The heat capacity of CO2(g) between 30 C and 100 C is given by the following equation Cp = 26.65+ 42.3x10-3 T/K-142.4X10 -7 T 2/K 2 in J K -1 mol -1 . a )Calculate the enthalpy change and b) the entropy change between 30C and 100 C.
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Calculate the change in the entropy of a system when going from a condition of 5 accessible microstates to 30 accessible microstates given that the Boltzman constant is 1.38x10 - 23 J/K. Express your result in scientific notation (e.g. the atoms in a mole are 6.022E23).
If the final temperature is 166.66K, determine the change in entropy for each substance.
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b) i. Define entropy. ii. 1.0 kg of water at 0 °C is mixed with an equal mass of water at 100 °C. After equilibrium is reached, the mixture has a uniform temperature of 50 °C. Calculate the change in entropy of the water. R= 8.31 kJ mol- K- and for water, Cy = 4186 J kg' K'.
Answer the following questions with complete/step-by-step solutions: (Note: The following problems are interconnected to each other.) Problem 1. A quantity of an ideal gas in an isolated system is expanded isothermally and reversibly at 400 degrees Kelvin from a volume V1 to V2. During the expansion the gas absorbs 200 calories of heat from the reservoir in contact with it. Find (a) the entropy change of the gas, (b) the entropy change of the reservoir and (c) the entropy change of the whole system. Problem 2. If the gas in problem 1 is expanded from V1 to V2 isothermally but irreversibly at 400 degrees Kelvin with an absorption of 100 calories of heat, what will be the entropy changes for (a) the gas, (b) the reservoir, (c) the complete system? Problem 3. Suppose the gas in problem 1 expands freely from V1 to V2 at 400 degrees Kelvin. What will be the entropy changes for (a) the gas, (b) the reservoir, and (c) the entire system?
the probabilities of states of independent systems X and Y are given by tables: xi x1 x2 pi 0,3 0,7 yi y1 y2 pi 0,4 0,6 find the entropy of the combined system (X, Y).