An aluminum bar of mass 2.00kg at 300?C is thrown into a lake. The temperature o

Question

An aluminum bar of mass 2.00kg at 300?C is thrown into a lake. The temperature of the water in the lake is 15.0?C; the specific heat capacity of aluminum is 900J/(kg?K) .

Part A

The bar eventually reaches thermal equilibrium with the lake. What is the entropy change ?Slake of the lake? Assume that the lake is so large that its temperature remains virtually constant.

Part C

Since the aluminum bar is not an isolated system, the second law of thermodynamics cannot be applied to the bar alone. Rather, it should be applied to the bar in combination with its surroundings (the lake).
Assume that the entropy change of the bar is -73.5J/K , what is the change in total entropy ?Stotal?

Explanation / Answer

The change in entropy of a system is equal to the change in the total enthalpy of the system divided by the temperature of the system, in an isothermal process.
i.e. delta S = delta Q/ T
Assuming that the heat transfer process between the aluminum and lake was adiabatic (no losses to the ambient), then the total heat lost by the aluminum equals the total heat gained by the lake.

Thus heat gained by the lake is (mass of Al) x (C of Al) x (change in T of Al)
= 2 x 900 x (300-15)
= 513KJ
Change in entropy of the lake = 513,000/(273+15) = 1781.25J/K

Change in total enthropy is the algebraic sum of the change in enthropies i.e. 1781.25 - 73.5 = 1707.75J/K

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.