# 1-st and 2-nd laws of Thermodynamics

1. Solve both of the following problems

a. A sample of an ideal gas has the following initial conditions V=15L, T=250K and P=1atm. It is compressed isothermally until the change in entropy is -5J/K. What are the final conditions?

b. Calculate the change in entropy when 50g of 80C water is poured into 100g of 10C water. Assume the container is insulated so that no heat is lost to the surroundings.

2. Consider a fertilized hen egg in an incubator, a constant T and P environment. In a few weeks it will hatch into a chick.

a. Consider the egg your thermodynamic system. Is it Open, closed or isolated?

b. In the fertilized egg the hen provided proteins, carbohydrates and fats are formed into a highly organized chick. Does the entropy of this system increase or decrease? Does this violate the 2nd law of thermodynamics?

https://brainmass.com/physics/heat-thermodynamics/laws-thermodynamics-618407

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1. Solve both of the following problems

a. A sample of an ideal gas has the following initial conditions V=15L, T=250K and P=1atm. It is compressed isothermally until the change in entropy is -5J/K. What are the final conditions?

b. Calculate the change in entropy when 50g of 80C water is poured into 100g of 10C water. Assume the container is insulated so that no heat is lost to the surroundings.

2. Consider a fertilized hen egg in an incubator, a constant T and P environment. In a few weeks it will hatch into a chick.

a. Consider the egg your thermodynamic system. Is it Open, closed or isolated?

b. In the fertilized egg the hen provided proteins, carbohydrates and fats are formed into a highly organized chick. Does the entropy of this system increase or decrease? Does this violate the 2nd law of thermodynamics?

Solutions:

1. (a) An isothermal compression requires a negative heat change, according to the 1-st law:

( 1)

Since (constant temperature), then

( 2)

The isothermal process is described by the equation

( 3)

By integrating, one yields:

( 4)

Compression means that ; it follows that , so that .

The process is assumed to be quasistatic, that is reversible. In this case, the entropy variation is due to the heat change only. Since the temperature is constant, one can write:

( 5)

where is the entropy change caused by the heat change with the surroundings.

Hence, the final volume of the gas can be found:

( 6)

Numerically:

(b) When mixing two quantities of water, every quantity will change its internal energy according to the temperature variation. By denoting the final temperature of the mixture (equilibrium temperature), the change of internal energies will be:

( 7)

where cv = specific heat of water at constant volume (or constant pressure, it is the same).

Since it is obvious that .

On the other hand, the container is insulated, so that no heat or work will be exchanged with surroundings. According to the first law (1), the total internal energy change of both water quantities will be zero:

( 8)

Introducing in (7), the final temperature of the mixture will be found:

( 9)

( 10)

Numerically:

( 11)

The entropy change of each water quantity is given by:

( 12)

( 13)

The total entropy variation will be:

( 14)

Numerically:

( 15)

(the total entropy variation is positive as the process is a natural, irreversible one).

2. (a) Since the shell of the egg is porous, the egg is an open thermodynamic system (otherwise, the egg were a "dead" matter). A transfer of gases occurs through the shell. Carbon dioxide and water is released through the pores, being replaced by air which includes oxygen.

(b) The egg is a complex thermodynamic system. Since at appropriate conditions the egg turns into a chick, that means that the entropy of the egg (as thermodynamic system) will decrease. However, this doesn't violate the 2-nd law.

The balance of entropy in an open system is described by equation:

( 16)

where Sirr is the irreversible entropy due to irreversible processes occurring in the egg, which always is positive according to 2-nd law.

Assuming that, at thermal equilibrium

( 17)

decreasing of entropy means

( 18)

Since , it follows that

( 19)

Thus, if an open system releases high entropy while absorbing law entropy, it is possible to decrease its entropy without violating the 2-nd law.

https://brainmass.com/physics/heat-thermodynamics/laws-thermodynamics-618407