Question

A constant pressure of 7 bar is applied to the piston of a frictionless moving piston-cylinder system and there is superheated water vapor with a volume of 0.05 dm3 at 300 °C. It is connected to a pipe with a valve at the bottom of the cylinder, through which hot water vapor at 20 bar and 400 °C passes. By opening the valve for a while, 0.07 kg of steam is taken into the cylinder as isothermal and isobaric.

1- Calculate the heat exchange.

2- Find the final mass and final volume of the steam in the cylinder and the volume work flowing into the environment during the process.

3- Calculate the entropy production of the water in the cylinder due to events other than matter and heat exchanges.

Answer 1

1- To calculate the heat exchange, we can use the equation Q = m × ΔH, where Q is the heat exchange, m is the mass, and ΔH is the enthalpy change.
First, we need to calculate the initial enthalpy of the superheated water vapor using steam tables or equations. Let's assume it to be h1.

Next, we need to find the final enthalpy of the steam after it is brought to the isothermal and isobaric state. Let's assume it to be h2. The mass of the steam is given as 0.07 kg.
Now, we can calculate the heat exchange using the equation Q = m × (h2 - h1).

2- To find the final mass and final volume of the steam in the cylinder, we can use the ideal gas equation: PV = mRT, where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature. Given that the pressure is 7 bar and the volume is 0.05 dm3, we can calculate the initial temperature using the ideal gas equation.
Next, we need to find the final temperature of the steam after it is brought to the isothermal state. Let's assume it to be T2. Using the final temperature, we can calculate the final volume using the ideal gas equation. To find the volume work flowing into the environment during the process, we can use the equation W = P × (V2 - V1).

3- To calculate the entropy production of the water in the cylinder due to events other than matter and heat exchanges, we can use the equation ΔS = m × (s2 - s1), where ΔS is the entropy change, m is the mass, and s is the specific entropy.
First, we need to calculate the initial specific entropy of the superheated water vapor using steam tables or equations. Let's assume it to be s1.

Next, we need to find the final specific entropy of the steam after it is brought to the isothermal and isobaric state. Let's assume it to be s2.
Now, we can calculate the entropy production using the equation ΔS = m × (s2 - s1).

Remember to substitute the given values into the equations and ensure that units are consistent throughout the calculations.