liquid water of mass 10 kg & temperature 20 degree celsius mixed with 2 kg of ice at -5 degree celsius till equilibrium is reached at 1 atm presssure . find entropy ??
104.5 kj/k
To find the change in entropy when liquid water and ice reach equilibrium, we need to calculate the entropy change for both substances separately and then combine them.
1. Entropy change of the liquid water:
The change in entropy (ΔS) for a substance is given by the equation:
ΔS = mcΔT/T
Where:
- ΔS is the change in entropy
- m is the mass
- c is the specific heat capacity
- ΔT is the change in temperature
- T is the initial temperature
Given:
- Mass of liquid water (m) = 10 kg
- Temperature change (ΔT) = final temperature - initial temperature
- Initial temperature (T) = 20°C
- Specific heat capacity of water (c) ≈ 4186 J/(kg·K) (at constant pressure)
Convert temperature from Celsius to Kelvin:
Initial temperature (T) = 20°C + 273.15 K = 293.15 K
Calculate the entropy change for the liquid water:
ΔS_water = (10 kg) * (4186 J/(kg·K)) * (ΔT) / (293.15 K)
2. Entropy change of the ice:
The change in entropy for a phase change (such as ice melting) is given by the equation:
ΔS = ΔH/T
Where:
- ΔS is the change in entropy
- ΔH is the enthalpy change (heat of fusion or heat of melting)
- T is the initial temperature
Given:
- Mass of ice (m) = 2 kg
- Initial temperature (T) = -5°C
- Heat of fusion (ΔH) for ice ≈ 334,000 J/kg (at 0°C)
Convert temperature from Celsius to Kelvin:
Initial temperature (T) = -5°C + 273.15 K = 268.15 K
Calculate the entropy change for the ice:
ΔS_ice = (2 kg) * (334,000 J/kg) / (268.15 K)
3. Total change in entropy:
Since entropy is a state function, we can add the entropy changes of water and ice to find the total change in entropy:
ΔS_total = ΔS_water + ΔS_ice
Calculate the total change in entropy.
Note: The calculation assumes that the pressure is constant and there are no other factors affecting the entropy change.