Argon gas enters an adiabatic turbine at 800^∘ C and 1.5 MPa at a rate of 80 kg / min and exhau

Argon gas enters an adiabatic turbine at 800^∘ C and 1.5 MPa...

Argon gas enters an adiabatic turbine at $800^{\circ} \mathrm{C}$ and $1.5 \mathrm{MPa}$ at a rate of $80 \mathrm{~kg} / \mathrm{min}$ and exhausts at $200 \mathrm{kPa}$. If the power output of the turbine is $370 \mathrm{~kW}$, determine the isentropic efficiency of the turbine.

Key Concepts

Steady Flow Energy Equation

The steady flow energy equation is a formulation of the first law of thermodynamics applied to a control volume. It accounts for the energy balance involving mass flow in and out of the device, work interactions, and changes in energy forms, and is essential for analyzing devices like turbines where mass flow and energy transfer are continuous.

Turbine Operation

A turbine is a rotating mechanical device that extracts energy from a fluid flow to produce work. Understanding its operation involves analyzing the fluid dynamics, energy transformations, and efficiency losses inherently present in the energy conversion process, which are often quantified using parameters like isentropic efficiency.

Isentropic Efficiency

Isentropic efficiency is a dimensionless measure that compares the actual work output of a turbine to the theoretical work output under ideal, reversible (isentropic) conditions. It quantifies the deviation of a real process from the most efficient process possible and is crucial in analyzing the performance and design of turbines.

Adiabatic Process

An adiabatic process is one in which no heat transfer occurs between the system and its surroundings. In the context of turbines or other thermodynamic devices, assuming an adiabatic process simplifies analysis by focusing solely on the work interactions and internal energy changes within the system.

Transcript

00:01 As given in this question is there's an organ gas that enters an adiabatic turbine.

00:11 So here we take the adiabatic turbine in which the organ gas enters with pressure of 1 .5 megapascal.

00:28 So we take this pressure as a p1 at temperature 800 degrees centigrade.

00:42 So we take this as t1.

00:48 At the rate of 80 kg per minute, which means rate of mass is given, that is 80 kg per minute.

01:02 And exhaust at 200 kiosk, which means the organ gas leaves at a specified pressure.

01:11 And that pressure is 200 kilo pascal and we take this pressure as b2 and the power output of this turbine is 370 kilowatt which means our w .a is 370 kilowatt so this is all our given data so what we have to find in our question ask that we have to find as entropic efficiency of the turbine so this would we have to find so now we start the solution as first of all we must know about the specific heat ratio of organ is k which is equals to 1 .666 7 double 67 and the constant pressure specific heat of argon is cp which is equals to 0 .5203 kilojou per kg into kelvin so this is our value for cp and we take it from table a so now there is only one inlet and and one exit so we take m our rate of m mass is m1 is equals to m2 which is equals to m dot so we take the asentropic turbine as a system which is the control volume since crosses the boundary so the energy balance for the steady flow system can be expressed as like this so here we're using the energy balance for this system so that is expressed as are the rate of energy in and the rate of energy out so this equals to our rate of a mass into h1 then our work as out plus rate of m h2 s as since our rate of heat of heat that equals to the rate of heat that equals to the the change of kinetic energy that approximately equals to rate of change of kinetic energy and then approximately equals to potential energy and this is approximately equals to 0.

04:49 So then our equation becomes like this, that our rate of a workout, that m dot h1 minus h2, our rate of a mass into h1 minus h2...

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