What does the area under a T-S curve on a Temperature vs. Entropy diagram represent?
The area under a T-S curve is the calculated heat rejected or absorbed into the system. In order to calculate the heat of the system, take the first derivative of the function to find the area under the curve.
Which cycle does an aircraft gas turbine operate on?
An aircraft gas turbine operates on the Brayton Cycle. The Brayton cycle is a thermodynamic cycle that describes the workings of a constant pressure heat engine. In order to analyze a Brayton Cycle, it is best to solve the problem as a closed system, with the assumption that the exhaust is fed back into the intake. When viewing the cycle on a T-S diagram, in which the four stages of the cycle are graphed with respect to temperature and entropy, the stages where the pressure is constant can be easily recognized as the sloped lines connecting stages 2 and 3, and 4 and 1. It is during these constant pressure stages in which heat is absorbed and released from the system. The four stages are described as 1) adiabatic compression 2) isobaric heat addition 3) adiabatic expansion 4) isobaric heat rejection
What is the second derivative of x^2?
The derivative of a function is the "rate of change." The first derivative, x' of x^2 can be found using the following formula: x' = n*x^(n-1). Therefore, the 1st derivative of x^2, when n=2 is: x' = (2)x^(2-1) = 2x. The second derivative of x^2 when n=1 is: x'' = 2x^(1-1) = 2.