Question

2 kg of water is contained in a piston cylinder, and it is initially a saturated vapor at 100 ∘C. The water is isothermally compressed until it reaches a pressure of 1 MPa. Assume liquid water is perfectly incompressible. Determine: The heat transfer

Answer 1

The heat transfer during the isothermal compression of 2 kg of water from a saturated vapor state at 100 °C to a pressure of 1 MPa is 2256 kJ.

Step-by-step explanation:

During isothermal compression, the temperature remains constant. Using the saturated vapor tables, we find the initial state of water at 100 °C. The specific enthalpy (ℎ) at this state is obtained. Since the process is isothermal, the final state is determined by the pressure of 1 MPa. The specific enthalpy at the final state is also determined. The heat transfer (Q) during the process is then given by the equation Q=m⋅(hf−hi), where m is the mass of water, hf is the final specific enthalpy, and hi is the initial specific enthalpy.

For this specific case, the mass of water (m) is given as 2 kg. The initial specific enthalpy (hi) is obtained from the saturated vapor tables at 100 °C. The final specific enthalpy (hf) is obtained at the pressure of 1 MPa. Plugging these values into the heat transfer equation yields the final answer of 2256 kJ. This represents the energy transferred as heat during the isothermal compression process.

The assumption of perfectly incompressible liquid water simplifies the calculations, and the isothermal nature of the process allows for a straightforward determination of heat transfer using the enthalpy values at the initial and final states.