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# Statistical Thermodynamics

Entropy is the least understood quantity in science, as are the laws that govern it. Avoid the pitfalls and understand entropy better than most working scientists.

# Zeroth law of thermodynamics

Initially, there are two very small, thermally isolated rooms $$A$$ and $$B.$$ The heat capacitance of room $$A$$ is $$40$$ quanta of energy and room $$A$$ contains $$32$$ quanta of energy. The heat capacitance of room $$B$$ is $$100$$ quanta of energy and room $$B$$ contains $$50$$ quanta of energy. When the two room are thermally connected, in which direction will the quanta flow, on average?

Calculate the temperature increase when $$400 \text{ J}$$ of heat is applied to $$46.8 \text{ g}$$ of $$\ce{NaCl}.$$

 Details and assumptions:

• The molar heat capacity for $$\ce{NaCl}$$ is $$C_p = 50 \text{ J} \cdot \text{mol}^{–1} \cdot \text{K}^{–1} .$$
• The formula weight of $$\ce{NaCl}$$ is $$58.5 \text{ g/mol}.$$

Initially, there are two thermally isolated rooms $$A$$ and $$B.$$ The heat capacitance of room $$A$$ is $$80$$ quanta of energy and room $$A$$ contains $$56$$ quanta of energy. The heat capacitance of room $$B$$ is $$80$$ quanta of energy and room $$B$$ contains $$24$$ quanta of energy.

Question: When the two rooms are thermally connected and allowed to approach equilibrium, how many quanta of energy are transferred, on average?

There are 2 beakers of water in a room. In one beaker, the temperature of water is $$11 ^\circ \text{C}$$ higher than room temperature, and the other is $$11 ^\circ \text{C}$$ lower than room temperature. Let them be on a table without contact with each other, then after enough time passes an equilibrium is reached. What is the difference between the temperatures of the waters in the beakers?

Two objects $$A$$ and $$B$$ with temperatures $$T_1 = 258 \text{ K}$$ and $$T_2 = 269 \text{ K},$$ respectively, are each in a closed system. They are brought into thermal contact and enough time passes. If the final temperature of both objects is $$T_f,$$ what is the relation between $$T_1,$$ $$T_2$$ and $$T_f?$$

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