Calculate the change in entropy of the cube-lake system

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To calculate the change in entropy of the cube-lake system, begin with the formula for the change in entropy, dS = dQ/T, where dQ is the heat transfer and T is the temperature. The ice cube will absorb heat from the lake until it reaches thermal equilibrium, which occurs when the ice cube melts and warms to 0°C before the water warms to 13°C. The heat required to raise the temperature of the ice cube from -20°C to 0°C and then to melt it must be calculated using the specific heat of ice. The lake's temperature remains effectively constant at 13°C due to its large mass compared to the ice cube. The total change in entropy is the sum of the entropy changes for both the ice cube and the lake as they reach equilibrium.
kukulalalu89
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A 11 g ice cube at -20°C is placed in a lake whose temperature is 13°C. Calculate the change in entropy of the cube-lake system as the ice-cube comes into thermal equilibrium with the lake. The specific heat of ice is 2220 J/kg*K. (Hint: Will the ice cube affect the temperature of the lake?)


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i have no idea how to calculate this... at all.. T_T
 
kukulalalu89 said:
A 11 g ice cube at -20°C is placed in a lake whose temperature is 13°C. Calculate the change in entropy of the cube-lake system as the ice-cube comes into thermal equilibrium with the lake. The specific heat of ice is 2220 J/kg*K. (Hint: Will the ice cube affect the temperature of the lake?)
Start by giving us the expression for the change in entropy dS due to an infinitessimal heat flow dQ.

What is the final temperature of the water molecules that are contained in the ice cube? Where does that heat flow come from?

How much heat has to flow? Use the expression for dS to work out the total entropy change for the lake.

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