Question

A piston-cylinder device initially contain 0.4 m3 of 1.8-kg saturated liquid water and steam mixture at 110 kPa. A electric heater in the device is turned on and passes a current of 1.7 A from a 120-V source. Only transfer of electrical work and boundary work exist. The piston initially rests on a set of stops, and a pressure of 200 kPa is required to move the piston. Afterwards the system continues to raise the piston and eventually reaches the temperature of 400 Celcius.

Find the initial quality of the system,initial internal energy (kj/kg), time it takes for the system to just move the piston (hours), final volume of system (m3), and total time it takes for the system to reach its final state (hours)

Answer 1

The quality of the steam can be calculated using the steam tables for the given pressure. I have attached the results for the given pressure of 110KPa -

Units Sl(bar) Input Data Steam Pressure 110 kPa abs Show Advanced Options Calculate Clear Result °C < < kJ/kg < Saturated Steam Temperature Latent Heat of Steam Specific Enthalpy of Saturated Steam Specific Enthalpy of Saturated Water Specific Volume of Saturated Steam Specific Volume of Saturated Water 102.292 2250.4 2679.18 428.775 1.54955 0.00104526 < kJ/kg kJ/kg m®/kg m®/kg

From the data given in the question the :

v1 = 0.4 m³

m1 = 1.8 kg

Therefore, the specific volume of the system is v1/m1 = v_s = 0.4/1.8 = 0.22

Therefore the quality of steam can be calculated with the help of the formula as :

5 07 X1= Ug - V1

where vl and vg are specific volumes of saturated water and saturated steam taken from the steam table.

Substituting the numericals in to the equation we get the quality of steam = X1 = 0.1428.

Similarly using the steam tables the internal energy of the system was calculated to be 2508.73 kJ/kg