Statistical Thermodynamics
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 \( T_f? \)