Consider two blocks of copper. Block A contains 800 atoms and initially has a total of 20 quanta of energy. Block B contains 200 atoms and initially has 80 quanta of energy. The two blocks are placed in contact with each other, inside an insulated container (so no thermal energy can be exchanged with the surroundings). After waiting for a long time (for example, an hour), which of the following would you expect to be true?
a. Approximately 50 quanta of energy are in block A, and approximately 50 quanta of energy are in block B.
b. Approximately 80 quanta of energy are in block A, and approximately 20 quanta of energy are in block B.
c. The entropy of block A is equal to the entropy of block B.
d. The temperature of block A and the temperature of block B are equal.

For the given condition in the paragraph, the statements (a) and (c) are false. And the statements given in option (b) and (d) are true.

Given data:

Number of atoms in Block A is, 800 atoms.

Initial amount of energy in Block A is, 20 quanta.

Number of atoms in Block B is, 200 atoms.

Initial amount of energy in Block B is, 80 quanta.

We will use the concept of Energy to relate it with the temperature, to solve the given problem. Also, there is some glance about the equilibrium condition as discussed:

Thus, we conclude that for the given condition, the statements (a) and (c) are false. And the statements given in option (b) and (d) are true.

Learn more about the thermal equilibrium here:

link

Option B and Option D are true

Explanation:

We are given;

Number of atoms in block A = 800

Energy content in block A = 20 quanta

Number of atoms in block B = 200

Energy content in block B = 80 quanta

The energy of a system which is an extensive quantity,depends on the mass or number of moles of the system. However, at equilibrium, the energy density of the two copper blocks will be equal. That is, each atom of Cu in the two blocks will, on average, have the same energy. Because block A has 4 times more atoms than block B, it will have 4 times more quanta of energy. Thus, option B is therefore true while option A is false.

Temperature is a measure of the average kinetic energy of the atoms in a material. Now, if each atom in blocks A and B have the same average energy, then the temperatures of blocks A and B will be equal at equilibrium. Thus, option D is true.

Entropy of a system is an extensive quantity that depends on the the mass or number of atoms in the system. Because block A is bigger than block B, it will have higher entropy. However, that the specific entropy (the entropy per mole or per unit mass) is an intensive quantity -- it is independent of the size of a system. The molar entropy of blocks A and B are equal at equilibrium. Thus option C is false.

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