Question

1. [40pts] We have a chamber filled with ideal gas of monatomic molecules. The chamber is thermally isolated from the surroundings: this chamber is then separated into two parts by a diathermal wall through which heat can flow The left chamber has a total energy E1 while the right chamber has a total energy Ez diathermal wall E1 E2 adiabatic wall (a) [5pts] If the number of possible states of the left chamber is Ω1(E1) and that for the right chamber is Ω2(E2), what is the total possible number of states Qotal of the whole system (b) [15pts] Derive the condition for equilibrium in terms Ω1(E1) and Ω2(E2) , i.e. number of states of each chamber, and its derivative with respect to E1 and/or E E E1tE2 is the total energy of the whole system which is conserved (c) [10pts] Using the above results, you can now define one of the key thermodynamic quantities, temperature (T). State the equilibrium conditions using this quantity, T. (d) [10pts] Examine how this newly-defined quantity control the flow of their conjugate quantity which is energy (E). For example, discuss the flow of energy when Ti>T2

Answer 1