Question

2.1 cubic metres of saturated liquid water at 200°C is expanded isothermally in a closed system until its quality is 85 percent. Determine the total work produced by this expansion, in kJ.

Answer 1

The total work produced by the isothermal expansion of saturated liquid water is 1,680,000 kJ.

Step-by-step explanation:

In this problem, we are given the initial volume and temperature of saturated liquid water, as well as the final quality after isothermal expansion. We can calculate the mass of the water using its density, and then use the specific heat capacity to calculate the change in internal energy. Finally, we can use the First Law of Thermodynamics to calculate the work done during the expansion.

First, let's calculate the mass of the water. Given a volume of 2.1 cubic meters and a density of 1,000 kg/m³, we have:

Mass = Volume * Density = 2.1 m³ * 1000 kg/m³ = 2100 kg

Next, we can calculate the change in internal energy using the specific heat capacity of water. Given a temperature change of 200°C, we have:

Change in Internal Energy = Mass * Specific Heat Capacity * Temperature Change = 2100 kg * 4000 J/kg/°C * 200°C = 1,680,000,000 J

Finally, we can calculate the work done during the expansion using the First Law of Thermodynamics. The work done is equal to the change in internal energy, so:

Work = Change in Internal Energy = 1,680,000,000 J = 1,680,000 kJ

Therefore, the total work produced by the expansion is 1,680,000 kJ.