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# Entropy

Entropy is a measure of the number of specific ways in which a system can be arranged. It is considered to be the measure of disorder. In an isolated system, entropy never decreases because isolated systems spontaneously evolve towards thermodynamic equilibrium which is the state of maximum entropy.

Entropy is a thermodynamic quantity that helps to account for the flow of energy through a thermodynamic process. Originally, entropy was defined by a thermodynamically reversible process as

Î”S = âˆ«(dQrev)/T

where entropy is found from the uniform thermodynamic temperature of a closed system divided into an incremental reversible transfer of heat into that system.

Entropy in thermodynamics is a non-conserved state function that has major importance in the science of physics and chemistry. The concept of entropy evolved in order to explain why some processes occur spontaneously while their time reversals do not. Systems tend to process in the direction of increasing entropy. Chemical reactions cause changes in entropy and entropy plays an important role in determining which direction a chemical reaction spontaneously proceeds.

### Carnot and heat engine

1. How much work is required, using an ideal Carnot refrigerator, to change 0.500 kg of tap water at 10.0Â°C into ice at -20.0Â°C? Assume the temperature of the freezer compartment is held at -20.0Â°C and the refrigerator exhausts energy into a room at 20.0Â°C. 2. A heat engine operates between two reservoirs at T2 = 600 K an

### Entropy change of the universe

5.9 Two equal quantities of water, of mass m and at temperatures T1, and T2, are adiabatically mixed together, the pressure remaining constant. Show that the entropy change of the universe is [see the attachment for the equation] where c_p, is the specific heat of water at constant pressure. Show that [delta]S >= 0. (Hint: (a

### Probability and Entropy

What is the change in entropy for the following "reactions"? For the purposes of this exercise treat the pennies as if this was about molecules and use Bolzmann's constant in your calculations. a. 100 pennies that were all arranged to be heads facing up and changed to all have tails facing up. b. 100 pennies that were arranged

### A descriptive account of how to deduce the magnitude of the entropy changes by considering two processes, the melting of 0.1 kg of ice to water and the heating of the water from 0 to 25 degrees C; a ;a latent heat change and a specific heat change

100 g of ice is melted at 0 degree C, and the resulting water is warmed to room temperature (25 degree C). Calculate delta S (change in entropy) for this whole process and comment on the relative magnitude of the entropy changes for the two steps. Explain the sign of delta S.

### Thermodynamics: Change in entropy

Only need to show part b. Two equal quantities of water, each of mass m and at temperatures T_1 and T_2 are diabatically mixed together, the pressure remaining constant. a. Show that the entropy change of the universe is: delta(S) = 2*m*Cp*ln[(T_1+T_2)/2sqrtT_1*T_2)] b. Show that delta(S) greate

### Physics: Entropy Increases Delta

Suppose that a system A is placed into thermal contact with a heat reservoir A' which is at an absolute temperature T' and that A absorbs an amount of heat Q in this process. Show that the entropy increase delta (S) of A in this process satisfies the inequality delta (S) >= Q/T' where the equals sign is only valid if the initial

### Entropy Change in Melting of Ice: Example Problem

A 10-2 kg ice cube, initially at zero degrees C, melts in the Atlantic Ocean, where the water temperature is at 10 degrees C. After melting, the ice melt heats up to match its 10 degree C environment. (The latent heat of fusion = 333J/g and the specific heat = 4.18 J/(g K). Find the change in entropy of (a) The water tha

### Entropy increase of Carnot engine operating on methane

A Carnot engine operates on 1 kg of methane, which we shall consider to be an ideal gas. Take Î³ = 1.35. The ratio of the maximum volume to the minimum volume is 4 and the cycle efficiency is 25 percent. Find the entropy increase of the methane during the isothermal expansion. Î³ = cp/cv Î· = .25 = 1-T1/T2 I know to co

### Carnot Cycle Efficiency in an Idea Gas

Please see the attached problem on how to show the efficiency of a Carnot cycle of an ideal gas using its entropy-temperature diagram. Maximum efficiency must then be estimated.

### Partition Function and Single-Particle System

Write down an expression for the partition function of a single-particle system. Show that the mean energy (E) is given by (E) = d ln Z / dB, Where Z is the partition function and Beta = 1/(k_B)(T). A one-dimensional quantum harmonic oscillator is in thermal equilibrium with a heat bath at temperature T. It has energy l

### Entropy of Noninteracting Distinguishable Oscillators

See attached file.

### Calculating entropy of water, reservoirs, and universe

I need some help with this problem. Here is the problem. Btw, this is problem #5.4 from Equilibrium Thermodynamics 3rd edition by C.J. Adkins 1*10^-3 m^3 of water is warmed from 20 to 100 degrees Celsius A) by placing it in contact with a large reservoir at 100 degrees Celsius, B) by placing it first in contact with a large r

### Change in entropy that the Universe has to suffer from Ice Cream melting?

If a carton of ice cream is left out of the freezer overnight and completely melts, how do I figure out what the change in entropy that the Universe has to suffer because of this? The mass of the ice cream = 1 kilogram Original temp. of ice cream was 0 deg. Celsius, but had heated up to 25 deg. Celsius (room temp.) The spec

### change in entropy of the ice/water

A one kilogram block of ice melts at 0Â°C and slowly warms up to the room temperature 30Â° C. (a) What is the change in entropy of the ice/water? Here's what I did: L_ice = Q/m = 80 cal/g = 80000 cal/1 kg deltaS_ice = Q/T = (80000)(4.186)/273 = 334880 J/273 K = 1226.67 J/K L_water = Q/m = 540 cal/1 g = 540000 cal

### Heat capacity and entropy

Experimental measurements of the heat capacity of aluminum at low temperature (below about 50 K) can be fit to the formula: See attached file for full problem description.

### Derive the formula for the multiplicity (entropy) of the two state paramagnet in the large N limit and when the number of excess spins relative to N is small.

For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N/2. (a) Use Stirling's approximation to estimate the height of the peak in the multiplicity function. (b) Derive a formula for the multiplicity function in the vicinity of the peak. (c) How wide is the peak in the m

### Expression for magnetic susceptibility of a magnetic solid is given. To determine the change in entropy with change in magnetic field at constant temperature.

The magnetic susceptibility per unit volume of a magnetic solid is given by x = A/(T-theta) where A and theta are constants independent of magnetic field. How much does the entropy per unit volume of this solid change if, at the temperature T, the magnetic field is increased from H = 0 to H = H_o?

### Microscopic Interpretation of Entropy

A box is seperated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured, and equilibrium is eventually attained. Assume that the volume of the b