IB Physics Entropy Change of Two Objects in Contact

/

A tutorial sheet on entropy change. Entropy change questions are often asked in HL Physics.

  1. If a quantity of heat Δq is added reversibly to a body at Kelvin temperture T then the increase of the entropy of the body is Δs defined by Δs=Δq/T.

  2. A reversible process is one where the body is in equilibrium at every stage of the process. In this case a small change in conditions may reverse the process exactly.In a reversible process the gain of entropy by one body is exactly equal to the loss of entropy by the other and the entropy of the whole system is unchanged.

  3. An irreversible process does not consist of equilibrium states at each stage of the process. An irreversible process creates entropy as the entropy gain by one body is greater than the entropy loss of the other.

  4. Two objects each of heat capacity C are placed in thermal contact. The final equilibrium temperature of both objects is T. Initially the temperature of the "hot" object is Th and the temperature of the "cold" object is Tc . Show that the change in entropy for the combined system is C ln(T2/(ThTc)). Assuming that all of the heat energy lost by the hot object is transferred to the cold object, show that Th = T + ΔT and Tc = T - ΔT. Hence show that the change in entropy for the system is C ln(T2/(T2-ΔT2)) and show that this is greater than 1. Use Δq = C Δθ where Δθ is the infinitesimal change in temperature. This problem is taken from Problems for Physics Students by K F Riley. The solution and additional notes on Boltzmann's constant can be found in the article by Jeffrey J Prentis in The Physics Teacher, vol 34, Oct 1996, pp 392-397.