Question

A rigid container contains 0.99m3 of saturated steam and 0.01m3 of

saturated liquid water at 95°C. Evaluate: a) The pressure of the
mix b) The quality of the mix. c) The enthalpy of the
mixture

Answer 1

The pressure of the saturated mixture at 95°C is slightly less than atmospheric pressure. The quality is the ratio of vapor volume to the total volume, and the enthalpy is calculated using this quality and the respective enthalpies of the saturated phases.

Step-by-step explanation:

The pressure of the mix in a rigid container containing saturated steam and saturated liquid water at 95°C can be determined using the thermodynamic properties of water at saturation conditions. Typically, this would involve consulting steam tables or thermodynamic charts that list properties like saturation pressure and temperature for water. However, without access to these specific values for 95°C, we can infer that since 100°C is the boiling point of water at 1 atm, the pressure at 95°C would be slightly less than 1 atm.

The quality of the mix (x) is the ratio of the mass of the vapor to the total mass of the mixture (both liquid and vapor). It can be calculated using the specific volumes of the saturated liquid (v_f) and the saturated vapor (v_g), along with the volumes of each phase in the mixture. The enthalpy (h) of the mixture can then be found by using the quality and the enthalpies of the saturated liquid (h_f) and saturated vapor (h_g).

Since the mixture is saturated at a given temperature, the pressure would be the saturation pressure corresponding to 95°C. The quality, x, is calculated by the formula x = (Vapor Volume) / (Total Volume) and the enthalpy of the mixture is h = (1 - x) * h_f + x * h_g, where h_f is the enthalpy of the saturated liquid and h_g is the enthalpy of the saturated vapor. These calculations would provide a quantifiable measure of the mixture's energy content.

Answer 2

a) The pressure of the mixture is 504.8 kPa.

b) The quality of the mixture is approximately 0.503.

c) The enthalpy of the mixture is approximately 1461.4 kJ/kg.

To evaluate the pressure of the mixture, we can use the concept of the total volume of the mixture. The total volume of the mixture is the sum of the volumes of the saturated steam and saturated liquid water. Given that the volume of the saturated steam is 0.99 m³ and the volume of the saturated liquid water is 0.01 m³, the total volume of the mixture is 0.99 m³ + 0.01 m³ = 1.00 m³.

To find the pressure of the mixture, we can use the steam tables for water and steam. The pressure of the mixture will be the saturation pressure corresponding to the temperature of the mixture. In this case, the temperature of the mixture is given as 95°C.

Using the steam tables, we find that the saturation pressure of steam at 95°C is approximately 504.8 kPa. Therefore, the pressure of the mixture is 504.8 kPa.

To evaluate the quality of the mixture, we need to determine the mass of the liquid water and the mass of the steam in the mixture. The quality, denoted as x, is defined as the ratio of the mass of steam to the total mass of the mixture.

Since the container is rigid, we can assume that the total mass remains constant. To find the mass of the liquid water, we can use the density of water at 95°C, which is approximately 958.4 kg/m³. The mass of the liquid water is then given by:

mass of liquid water = density of water × volume of liquid water
= 958.4 kg/m³ × 0.01 m³
= 9.584 kg

To find the mass of the steam, we can use the specific volume of steam at 95°C, which is approximately 0.102 m³/kg. The mass of the steam is then given by:

mass of steam = volume of steam / specific volume of steam
= 0.99 m³ / 0.102 m³/kg
≈ 9.706 kg

Therefore, the total mass of the mixture is approximately 9.584 kg + 9.706 kg = 19.290 kg.

The quality of the mixture, x, is then given by:

x = mass of steam / total mass of mixture
= 9.706 kg / 19.290 kg
≈ 0.503

Therefore, the quality of the mixture is approximately 0.503.

To evaluate the enthalpy of the mixture, we need to find the enthalpy of the liquid water and the enthalpy of the steam at the given temperature. Using the steam tables, we find that the enthalpy of the liquid water at 95°C is approximately 419.0 kJ/kg and the enthalpy of the steam at 95°C is approximately 2675.1 kJ/kg.

The enthalpy of the mixture is then given by the mass-weighted average of the enthalpies of the liquid water and steam:

enthalpy of mixture = (mass of liquid water × enthalpy of liquid water + mass of steam × enthalpy of steam) / total mass of mixture
= (9.584 kg × 419.0 kJ/kg + 9.706 kg × 2675.1 kJ/kg) / 19.290 kg
≈ 1461.4 kJ/kg

Complete question :-

A rigid container contains 0.99m3 of saturated steam and 0.01m3 of saturated liquid water at 95°C. Evaluate: a) The pressure of the mix b) The quality of the mix. c) The enthalpy of the mixture