Final answer:
The amount of heat transferred while heating steam in a rigid tank from 320°C to 540°C at constant pressure can be calculated using the mass of steam, specific enthalpy values, and the relationship ∆H = m • Cp • ∆T.
Step-by-step explanation:
The question deals with the heat transfer involved in heating steam within a rigid tank from an initial temperature of 320°C to a final temperature of 540°C while maintaining a constant pressure of 2MPa. The amount of heat transferred can be found by using the concept of enthalpy (specific enthalpy of steam) and the mass of the steam. Although the mass is not provided, this can be calculated since the initial state of the steam is known, and steam tables or thermodynamic equations can be used to find the enthalpy for both the initial and final states.
One can calculate the mass of steam in the initial state using the ideal gas law or more accurate methods such as the Van der Waals equation of state, but for this particular scenario, we would rely on steam tables given the high pressure and temperatures involved. Usually, these calculations involve looking up the specific enthalpy values at the given pressures and temperatures, and then using these to determine the heat added by the relationship:
∆H = m • Cp • ∆T
Where ∆H is the change in enthalpy, m is the mass of the steam, Cp is the specific heat at constant pressure, and ∆T is the change in temperature. This assumes that you can maintain pressure while heating the steam, which is realistic given the presence of the pressure regulator that allows some steam to escape to maintain the specified pressure.