What is the necessary and sufficient condition for exactness?

Equation (8.1) serves as both a necessary and sufficient condition for the exactness of a differential equation of the form M(x, y)dx + N(x, y)dy = 0. This implies that if the equation M(x, y)dx + N(x, y)dy = 0 is exact then equation (8.1) must be true (necessity).

How do you test for exactness?

What is differential condition?

a classical conditioning experiment in which two or more stimuli are used, each paired with different outcomes. The usual outcome is that a conditioned response is elicited by the positive conditioned stimulus but not by the other stimulus. …

How do you solve exact de?

What do you mean by homogeneous function?

Homogeneous function is a function with multiplicative scaling behaving. The function f(x, y), if it can be expressed by writing x = kx, and y = ky to form a new function f(kx, ky) = knf(x, y) such that the constant k can be taken as the nth power of the exponent, is called a homogeneous function.

What is Cauchy differential equation?

In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler’s equation is a linear homogeneous ordinary differential equation with variable coefficients. … Because of its particularly simple equidimensional structure the differential equation can be solved explicitly.

What is meant by inexact differential?

An inexact differential or imperfect differential is a type of differential used in thermodynamics to express changes in path dependent quantities. … Inexact differentials are primarily used in calculations involving heat and work because they are path functions, not state functions.

What is exact solution numerical analysis?

An exact solution is a symbolic representation of a value which solves a given equation exactly, while a numerical solution is numerical (often decimal) representation of a value which solves a given equation exactly or approximately. There are cases where these overlap, and cases where they are entirely different.

What is exact differential in chemistry?

An exact differential such as means that there exists a state function such that its differential is . An inexact differential such as and , does not hold this property. … If a system is in thermodynamic equilibrium than d Q / T is the exact differential of the entropy .

Why do path functions have inexact differentials?

So properties are called Exact Differentials or Point functions. But in case of Heat transfer and Work transfer, the quantity of heat and work transfer between state 1 and state 2 depends on the path followed. Therefore heat and work transfer are not exact differentials,they are Inexact differentials or path functions.

Why is heat an inexact differential?

Heat is an inexact differential in thermodynamics because it is a path dependent not state dependent i.e . it is a path funcion not state function just the work.

How do you solve an inexact differential equation?

What happens during a throttling process?

The throttling effect is to reduce the inlet pressure by a constant enthalpy process (represented by horizontal line AB). The result is a loss in entropy and also a slight fall in temperature with some reduction in the available heat drop. This accounts for a small loss in efficiency.

What do you understand by point function and path function What are exact and inexact differentials?

A Path function is a function whose value depends on the path followed by the thermodynamic process irrespective of the initial and final states of the process. … Work done in a thermodynamic process is dependent on the path followed by the process. A path function is an inexact or imperfect differential.

How do you integrate inexact differential?

Integrating factor μ=μ(ω), we get from equation dμμ=My−NxωxN−ωyMdω. By replacing known values M=2xy3+y4, My=6xy2+4y3, N=xy3−2y, Nx=y3 into equation, we have dμμ=6xy2+3y3ωx(xy3−2y)−ωy(2xy3+y4)dω.

What is throttling air?

A throttling device acts to restrict the flow of refrigerant at a point between the condenser unit and the evaporator. … This change in pressure is what allows the refrigerant to absorb the maximum amount of heat once it has entered the evaporator.

What is throttling process with example?

An example of a throttling process is an ideal gas flowing through a valve in mid position. … Because mass flow is constant, the change in specific volume is observed as an increase in gas velocity, and this is verified by our observations.

Is throttling isothermal?

This equation tells us that, in the case of negligible change in specific kinetic energy, the throttling of an ideal gas is an isothermal process.

What is the throttle body?

In a traditional spark ignition gasoline engine, the throttle body is the part of the air intake system that controls the amount of air that flows into an engine’s combustion chamber. … This process effectively controls the speed of the engine and ultimately, the speed of the vehicle.

What does it mean to throttle a fluid?

A throttle is the mechanism by which fluid flow is managed by constriction or obstruction.

What is a throttling valve?

A: Throttling valves are a type of valve that can be used to start, stop and regulate the flow of fluid through a rotodynamic pump. … With the throttling valve control method, the pump runs continuously, and a valve in the pump discharge line is opened or closed to adjust the flow to the required value.