A 298.0 kg block of ice at 0 C is placed in a large lake. The temperature of the lake is just slightly higher than 0 C, and the ice melts. What is the entropy change of the ice (in kJ/K)?
What is the entropy change of the lake (in kJ/K)?
What is the entropy change of the "universe", that is, of the ice plus the lake (in kJ/K)?
To calculate the entropy change of the ice, lake, and the universe, we need to consider the change in entropy using the formula:
ΔS = Q/T
Where:
ΔS is the change in entropy
Q is the heat transfer
T is the temperature in Kelvin
Let's start with the entropy change of the ice.
1. Entropy Change of the Ice:
The ice transforms from a solid state to a liquid state during melting. The heat transfer required for this change is given by:
Q = m * Lf
Where:
m is the mass of the ice (298.0 kg)
Lf is the latent heat of fusion, which is the amount of heat required to convert 1 kg of solid substance into the liquid state at constant temperature and pressure. For ice, Lf is approximately 334 kJ/kg.
Now, we need to convert the temperature from Celsius to Kelvin:
T = 0 + 273.15 = 273.15 K
Using the formula ΔS = Q/T, we can calculate the entropy change of the ice:
ΔS_ice = (m * Lf) / T
ΔS_ice = (298.0 kg * 334 kJ/kg) / 273.15 K
Calculating this gives us the entropy change of the ice.
2. Entropy Change of the Lake:
The entropy change of the lake can be calculated using the same formula, considering the heat transfer absorbed by the lake when it is in contact with the melting ice.
Since the temperature of the lake is just slightly higher than 0°C, we can assume it is approximately equal to 0°C. Converting this to Kelvin:
T = 0 + 273.15 = 273.15 K
Using the formula ΔS = Q/T, we can calculate the entropy change of the lake.
3. Entropy Change of the Universe:
To find the entropy change of the universe, we need to sum up the entropy changes of the ice and the lake:
ΔS_universe = ΔS_ice + ΔS_lake
Calculating this will give us the entropy change of the universe.
Please note that I have provided the general approach to calculating the entropy change. To get the specific numerical values, you can substitute the given values into the formulas and perform the calculations.