Compute the entropy change of a system consisting of 1kg of ice at 0•C which melts (reversibly) to water at the same temperature. The latent heat of melting is 79.6 Cal/g
To compute the entropy change of the system, we need to consider the entropy change during the phase transition (melting) and the entropy change when the temperature remains constant (0°C).
First, let's calculate the entropy change during the phase transition:
1. Convert the latent heat of melting from calories (Cal) to joules (J) using the conversion factor: 1 Cal = 4.184 J.
Latent heat of melting = 79.6 Cal/g * 4.184 J/Cal = 332.6064 J/g
2. Calculate the heat required to melt 1 kg of ice:
Heat required = mass of ice * latent heat of melting
Heat required = 1 kg * 332.6064 J/g = 332.6064 kJ
3. Now, calculate the entropy change during the phase transition:
Entropy change during melting = heat required / temperature
Entropy change during melting = 332.6064 kJ / 273 K = 1.2176 kJ/K
Next, let's calculate the entropy change when the temperature remains constant (0°C):
The entropy change when the temperature remains constant for an ideal substance is given by the formula:
ΔS = mc ln(T₂/T₁), where m is the mass, c is the specific heat capacity, T₁ is the initial temperature, and T₂ is the final temperature.
Since the temperature remains constant at 0°C, the entropy change in this case is zero, as ln(1) = 0.
Now, we can compute the total entropy change:
Total entropy change = entropy change during melting + entropy change at constant temperature
Total entropy change = 1.2176 kJ/K + 0
Total entropy change ≈ 1.2176 kJ/K
Therefore, the entropy change of the system is approximately 1.2176 kilojoules per Kelvin (kJ/K).
To compute the entropy change, ΔS, we can use the formula:
ΔS = m * ΔH / T
Where:
m = mass of the substance
ΔH = latent heat of melting
T = temperature at which the phase change occurs
Given:
m = 1 kg
ΔH = 79.6 Cal/g
T = 0°C = 273 K (since temperatures need to be in Kelvin in thermodynamics)
Converting the units of ΔH:
ΔH = 79.6 Cal/g * (1 kg / 1000 g) = 0.0796 Cal/g
Now we can substitute the values into the formula:
ΔS = m * ΔH / T
ΔS = 1 kg * 0.0796 Cal/g / 273 K
Calculating the entropy change:
ΔS = 0.0796 / 273
ΔS ≈ 0.00029 Cal/K
Therefore, the entropy change of the system is approximately 0.00029 Cal/K.