A. The mass of saturated liquid is 204.797 kg
B. The mass of saturated vapor is 68.266 kg
C. The percent of the total volume occupied by the saturated liquid is 14.375%.
Given:
A 1.4 m³ tank holds a two-phase liquid-vapor mixture of carbon dioxide at -17°C.
The quality of the mixture is 75%.
For saturated carbon dioxide at -17°C, vf = 0.9827 × 10⁻³ m³/kg and va = 1.756 × 10⁻² m³/kg.
(a) Determine the mass of saturated liquid.
The mass of saturated liquid can be calculated using the following equation:
m_liquid = x * m
where:
m_liquid is the mass of saturated liquid (kg)
x is the quality of the mixture (0.75)
m is the total mass of the mixture (kg)
To find the total mass of the mixture, we can use the following equation:
m = V / (x * vf + (1 - x) * va)
where:
V is the volume of the tank (1.4 m³)
vf is the specific volume of saturated liquid (0.9827 × 10⁻³ m³/kg)
va is the specific volume of saturated vapor (1.756 × 10⁻² m³/kg)
Substituting the given values into the equation, we get:
m = 1.4 m³ / (0.75 * 0.9827 × 10⁻³ m³/kg + (1 - 0.75) * 1.756 × 10⁻² m³/kg) = 273.0628 kg
Therefore, the mass of saturated liquid is:
m_liquid = 0.75 * 273.0628 kg = 204.797 kg
(b) Determine the mass of saturated vapor.
The mass of saturated vapor can be calculated using the following equation:
m_vapor = (1 - x) * m
where:
m_vapor is the mass of saturated vapor (kg)
x is the quality of the mixture (0.75)
m is the total mass of the mixture (kg)
We already found that the total mass of the mixture is 273.0628 kg. Substituting this value and the value of x into the equation, we get:
m_vapor = (1 - 0.75) * 273.0628 kg = 68.266 kg
Therefore, the mass of saturated vapor is:
m_vapor = 68.266 kg
(c) Determine the percent of the total volume occupied by the saturated liquid.
The percent of the total volume occupied by the saturated liquid can be calculated using the following equation:
percent_liquid_volume = (m_liquid * vf) / V * 100%
where:
percent_liquid_volume is the percent of the total volume occupied by the saturated liquid (%)
m_liquid is the mass of saturated liquid (204.797 kg)
vf is the specific volume of saturated liquid (0.9827 × 10⁻³ m³/kg)
V is the volume of the tank (1.4 m³)
Substituting the given values into the equation, we get:
percent_liquid_volume = (204.797 kg * 0.9827 × 10⁻³ m³/kg) / 1.4 m³ * 100% = 14.375%