10gm of steam 100°c are blown on the surface of 90gm water at 0°c contained in a calorimeter of water 10gm.all steams are condensed .calculate the increase in entropy of the system
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To calculate the increase in entropy of the system, we need to determine the change in entropy of each component and then sum them up.
1. Change in entropy of water:
The entropy change of water can be calculated using the equation:
ΔS = m*C*ln(T2/T1)
where:
ΔS = change in entropy
m = mass of the water
C = specific heat capacity of water (4.18 J/g°C)
T1 = initial temperature
T2 = final temperature
ΔS_water = 90g * 4.18 J/g°C * ln((100+273)/(0+273))
Convert temperatures to Kelvin:
ΔS_water = 90g * 4.18 J/g°C * ln(373/273)
ΔS_water ≈ 101.16 J/K
2. Change in entropy of steam:
The change in entropy of steam can be calculated using the equation:
ΔS = m*C*ln(T2/T1)
where:
ΔS = change in entropy
m = mass of the steam (10g)
C = specific heat capacity of steam (2.03 J/g°C)
T1 = initial temperature (100°C)
T2 = final temperature (100°C, since all steam condenses)
ΔS_steam = 10g * 2.03 J/g°C * ln(100/100)
ΔS_steam = 0 J/K (since ln(1) = 0)
3. Change in entropy of calorimeter:
The change in entropy of the calorimeter can be calculated using the equation:
ΔS = m*C*ln(T2/T1)
where:
ΔS = change in entropy
m = mass of the calorimeter (10g)
C = specific heat capacity of the calorimeter (4.18 J/g°C)
T1 = initial temperature (0°C)
T2 = final temperature (100°C)
ΔS_calorimeter = 10g * 4.18 J/g°C * ln(100/0)
ΔS_calorimeter ≈ 1248.87 J/K
Total change in entropy of the system can be calculated by summing up the changes in entropy of each component:
ΔS_system = ΔS_water + ΔS_steam + ΔS_calorimeter
ΔS_system = 101.16 J/K + 0 J/K + 1248.87 J/K
ΔS_system ≈ 1350.03 J/K
Therefore, the increase in entropy of the system is approximately 1350.03 J/K.
To calculate the increase in entropy of the system, we need to consider the entropy change for both the steam and water.
1. Entropy change for the steam:
The entropy change for the steam can be calculated using the formula:
ΔS₁ = (m₁ * S₁ - m₁ * S₀) + (m₂ * S₁ - m₂ * S₀)
Where:
ΔS₁ = Entropy change for steam
m₁ = Mass of steam
m₂ = Mass of condensed water
S₁ = Entropy of vaporization of water
S₀ = Entropy of saturated steam at the initial temperature
The values needed for the calculation are:
m₁ = 10 g
m₂ = m₁ (since all steam is condensed)
S₀ = Entropy of saturated steam at 100°C (can be obtained from tables or steam properties)
S₁ = Entropy of vaporization of water at 100°C (can be obtained from tables or steam properties)
2. Entropy change for the water:
The entropy change for the water can be calculated using the formula:
ΔS₂ = m₃ * Cp * ln(T₂ / T₁)
Where:
ΔS₂ = Entropy change for water
m₃ = Mass of water
Cp = Specific heat capacity of water
T₁ = Initial temperature of water
T₂ = Final temperature of water (assuming it reaches thermal equilibrium)
The values needed for the calculation are:
m₃ = 90 g
Cp = Specific heat capacity of water (approximated to around 4.18 J/g°C)
T₁ = 0°C
T₂ = 100°C (since all the heat is transferred from steam to water)
Once you have calculated ΔS₁ and ΔS₂, you can find the total entropy change by adding them together:
ΔS_total = ΔS₁ + ΔS₂
Note: Calculating the entropies requires knowing the entropy values at different conditions, which can be found from steam tables or thermodynamic databases.