### Entropy Change in Adiabatic Heat Exchange

A lump of copper having a mass of 10 gm at a temperature of 500oC is just dropped into a well insulated bucket containing 100 gm of water at a temperature of 50oC. If the heat capacities of copper and water are 0.095 and 1.0 respectively, expressed as cal/gm.oC, calculate the total change in entropy resulting from the process.

Calculations:

Final temperature of copper and water will be the same, and is obtained by enthalpy balance.

Heat lost by copper = heat gained by water

[mCP(T1 - T2)]Copper = [mCP(T2 - T1)]Water

10 x 0.095 x (500 - T2) = 100 x 1 x (T2 - 50)

0.95 x (500 - T2) = 100 x (T2 - 50)

(500 - T2) = 105.26 x (T2 - 50)

500 + 5263.2 = 106.26 T2

T2 = 54.2oC

Entropy change is given by

DS = m CP ln (T2/T1)

Where m is mass; CP is specific heat; T1 and T2 are initial and final temperatures respectively.

Entropy change of copper:

T1 = 273 + 500 = 773 K

T2 = 273 + 54.2 = 327.2 K

DSCopper = 10 x 0.095 x ln (327.2/773) = -0.817 cal/oC

Entropy change of water:

T1 = 273 + 50 = 323 K

T2 = 273 + 54.2 = 327.2 K

DSWater = 100 x 1 x ln (327.2/323) = 1.292 cal/oC

Total entropy change = DSCopper + DSWater = -0.817 + 1.292 = 0.475 cal/oC

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