Classical Mechanics

Statistical Thermodynamics

Zeroth law of thermodynamics

         

Initially, there are two very small, thermally isolated rooms A A and B. B. The heat capacitance of room A A is 40 40 quanta of energy and room A A contains 32 32 quanta of energy. The heat capacitance of room B B is 100 100 quanta of energy and room B B contains 50 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 J 400 \text{ J} of heat is applied to 46.8 g 46.8 \text{ g} of NaCl.\ce{NaCl}.

Details and assumptions:

  • The molar heat capacity for NaCl\ce{NaCl} is Cp=50 Jmol1K1. C_p = 50 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} .
  • The formula weight of NaCl\ce{NaCl} is 58.5 g/mol. 58.5 \text{ g/mol}.

Initially, there are two thermally isolated rooms A A and B. B. The heat capacitance of room A A is 80 80 quanta of energy and room A A contains 56 56 quanta of energy. The heat capacitance of room B B is 80 80 quanta of energy and room B B contains 24 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 11C 11 ^\circ \text{C} higher than room temperature, and the other is 11C 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 A and B B with temperatures T1=258 K T_1 = 258 \text{ K} and T2=269 K, 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 Tf, T_f, what is the relation between T1, T_1, T2 T_2 and Tf? T_f?

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