To calculate the increase in entropy when ice at -10°C is converted into steam at 100°C
To calculate the increase in entropy when ice at -10°C is converted into steam at 100°C, we need to consider each phase transition and calculate the entropy change for each step.
First, we need to calculate the entropy change when the ice is heated from -10°C to 0°C, undergoing a phase transition from solid to liquid.
ΔS_1 = ∫(C_p / T) dT
Here, Cp is the heat capacity of ice, and T is the temperature. The integration is performed from -10°C to 0°C.
Next, we need to calculate the entropy change when the liquid water is heated from 0°C to 100°C.
ΔS_2 = ∫(C_p / T) dT
Here, Cp is the heat capacity of liquid water, and T is the temperature. The integration is performed from 0°C to 100°C.
Finally, we need to calculate the entropy change when the liquid water is converted into steam at 100°C.
ΔS_3 = ΔH_vap / T
Here, ΔH_vap is the enthalpy of vaporization of water, and T is the temperature.
The total change in entropy is the sum of ΔS_1, ΔS_2, and ΔS_3.
ΔS_total = ΔS_1 + ΔS_2 + ΔS_3