 Hello and welcome to another video in the understanding thermodynamics video series. My name is Adrian and today we are looking at steady state open systems. In the previous two videos we said that we use the property enthalpy to denote the energy content of a flowing stream. Entalpy take both the internal energy and flow energy of the component into account. We then determine enthalpy for real substances, ideal and perfect gases. We also said that in an open system mass flow can take place across the system boundary. Now in this video we are going to apply the first law on a special type of open system namely steady state open systems. Firstly we are going to define a steady state open system and then we are going to apply the first law in two example questions. Let's consider the turbine engine of an aeroplane. Sometime after the plane has achieved cruising altitude the operating conditions of the engine will remain fairly constant and remain so for the duration of the flight which can last several hours. Our system in this case the aircraft engine comprises a specific region in space and can therefore be seen as an open system which can also be called a control volume. For steady state open systems we assume the following. Our coordinate frame moves with the airplane and therefore the control volume is stationary with regards to the coordinate frame. The temperatures and pressures inside the engine remain constant over time and the temperature and pressure of the air flowing into and out of the engine does not change with time. The mass flow rate of the air flowing through the engine does not change with time and therefore we can say there will be no accumulation of mass inside the engine and the rate at which mass flows out of the engine will be the same as the rate at which it flows into the engine. Also the rate at which energy flows out of the control volume will be the same as the rate at which energy enters the control volume. Now let's look at this visually. The system boundary is given by the green dashed line. For steady state we know that the mass flow rate in is equal to the mass flow rate out of the system. We also know that energy flow rate in is equal to the energy flow rate out. Static energy, potential energy and enthalpy are the forms of energy associated with the substance flowing across the system boundary either into or out of the system. Note that when we multiply mass flow in kilograms per second with enthalpy in kilojoules per kilogram we get the resulting units of kilowatts. Alright so let's do an example. The question states that air at 300 Kelvin and 100 kilo Pascal flows to a compressor at 2 kilograms per second and is compressed to a pressure of 200 kilo Pascal. The temperature at the outlet is 380 Kelvin and we need to go and calculate the power required by the compressor. We can make some assumptions by stating that air is an ideal gas in this case and is thus independent of pressure. Let us consider a photo of an air compressor. Here we have the inlet where air enters the compressor. The veins of the compressor are mounted on the shaft rotating at high speed driven by a power source such as an electric motor or a steam turbine which will be connected to the shaft. Due to the vein movement the air flows from left to right and is compressed until it reaches the outlet of the compressor here. The velocity of the air is relatively low as high velocities will cause vibration of the veins. Therefore we usually assume the kinetic energy of the air flowing in as well as out of the turbine is low and can be safely ignored. Also our problem does not give us any data with which you can calculate kinetic energy not of the air entering nor of the air leaving the turbine. You will also note that the inlet and outlet of the compressor is at the same elevation and therefore potential energy will not change and we do not take it into consideration. Again the problem statement anyway does not give us any information that will enable us to calculate the change in potential energy. Lastly the rate of heat loss or gain will be much smaller than the rate at which energy flows through the system and we usually assume that compresses and turbines are adiabatic which means it does not exchange heat with the surroundings and the problem statement does not give us any information which you can use to calculate heat loss or gain anyway. We can now represent the flow of mass and energy schematically. The red dashed line is the system boundary and we can write down the mass and energy balance using this boundary. The mass flow rate of the air in is equal to the mass flow rate out. Energy is associated with the air flowing across the system boundary into the system as well as the mechanical energy that is provided by the rotating shaft. These are the only streams of energy crossing the system boundary into the system. Energy leaves the system in the form of high temperature high pressure air crossing the system boundary and we know the mass flow rate of air and we can find the values of enthalpy for the air in and out of the system using the table ideal gas properties of air. Now calculate the power required to compress the air and we get an answer of 161.2 kilowatts. See if you get the same answers. Let's do another example focusing on a heat exchanger. So in a heat exchanger heat is transferred from a hot fluid to a colder fluid. For instance the radiator of your car heat is transferred from the hot cooling water to the ambient air. Again we assume that we can safely ignore the kinetic and potential energy of the streams and again we assume the heat loss or gain is much smaller than the rate at which energy flows through the system. For the system enclosed by the red dashed line we can now do an energy balance and write down the energy streams into the system and equate that to the energy streams out of the system. Energy enters the system with the hot fluid in and also with the cold fluid going in. The sum of these two energy terms are equal to the energy leaving the system with the hot fluid and the cold fluid. After some rearrangement the following equation results. And the equation shown here in the green box is equal to the rate of change of energy of the hot fluid. Alright now let's consider the following example. Water flows through the radiator of a car at 0.6 kilograms per second and is cooled from 85 degrees to 70 degrees Celsius. The atmospheric air flowing through the radiator is heated from 280 Kelvin to 320 Kelvin. Calculate the mass flow rate of the air and the heat transfer rate. Flow of air and water is given in the equation information. The water is cooled and the air is heated. The equation from the previous slide can therefore be used to calculate the mass flow rate of the air and the heat transfer rate. So we can read the values for the enthalpy of water and air from the tables. Water is a compressed liquid and we use the value of enthalpy of saturated liquid water at the same temperature. For air we use the table ideal gas properties of air. We can now calculate the value of the air flow rate and obtain a value of 0.94 kilograms per second. We can also calculate the value using specific heats for air and liquid water as shown here and arrive at the same value. See if you get the same answer as me using these two different approaches. Right to summarize. Open systems are also called control volumes. For steady state operation we assume that the condition inside our control volume does not change with time. There are therefore no accumulation of mass or energy and that the condition of the inlet and outlet streams also do not change with time. Therefore we can do a mass balance of the total mass flow rate in equals the total mass flow rate out of the system. And the energy flow rate into the system is also equal to the energy flow rate out of the system. Usually we ignore kinetic and potential energy and it would be clear from the problem statement whether it needs to be taken into consideration or not. In the course notes two examples are done to illustrate this and examples of typical steady state open systems are also discussed. Thank you very much for watching. Course notes are available on my website www.aronsblock.com. I'm also available on Twitter if you want to connect with me and ask any questions. See you in the next video. Bye.