What is the change in entropy of steam 320g of steam at 100°C when it is condensed to water at 100°C?
The change in entropy of steam 320g of steam at 100°C when it is condensed to water at 100°C is -2.09 kJ/K.
To find the change in entropy when steam is condensed to water, we need to use the formula:
ΔS = mL/T
Where:
ΔS = change in entropy
m = mass of the substance
L = latent heat of transformation
T = temperature
First, we need to find the latent heat of vaporization (L) for steam. The latent heat of vaporization for water is approximately 2260 kJ/kg.
Next, we need to convert the mass of steam from grams to kilograms. Since 1 kilogram is equal to 1000 grams, we have:
mass of steam = 320g = 320/1000 = 0.32 kg
Now we can calculate the change in entropy:
ΔS = mL/T
= (0.32 kg) * (2260 kJ/kg) / (100°C)
= 0.32 * 2260 / 100
≈ 7.232 kJ/°C
Therefore, the change in entropy of 320g of steam at 100°C when it is condensed to water at 100°C is approximately 7.232 kJ/°C.
To calculate the change in entropy when steam is condensed to water at the same temperature, we need to use the formula:
ΔS = m × ΔH / T
where:
ΔS is the change in entropy,
m is the mass of the substance,
ΔH is the change in enthalpy, and
T is the temperature.
In this case, we are given the mass of steam as 320g and the change in temperature is 100°C (since the steam is at 100°C and then condensed to water at the same temperature).
Now, we need to find the change in enthalpy for the phase change from steam to water. This can be obtained from a table or reference source, such as a steam table or heat of vaporization data. The heat of vaporization for water is approximately 40.7 kJ/mol.
To convert the mass of steam into moles, we can use the molar mass of water, which is approximately 18 g/mol. Therefore, the number of moles of water is:
n = mass / molar mass
n = 320g / 18g/mol ≈ 17.78 mol
The change in enthalpy for the phase change is then given by:
ΔH = n × ΔHv
ΔH = 17.78 mol × 40.7 kJ/mol ≈ 723.95 kJ
Finally, we can substitute the values into the formula to calculate the change in entropy:
ΔS = (320g / 18g/mol) × (723.95 kJ) / (100°C + 273.15 K)
ΔS ≈ 4.98 kJ/K
Therefore, the change in entropy of the steam when it is condensed to water at 100°C is approximately 4.98 kJ/K.