First Law for A Control Volume P M V Subbarao Professor Mechanical Engineering Department Modeling of True Engineering Systems…..

Laws of Nature for A Control Mass Conservation of Mass : Conservation of Momentum : First law of thermodynamics :

Rate Equations for Laws of Nature for A Control Mass Conservation of Mass : Conservation of Momentum : First law of thermodynamics :

The Family of Thermodynamic Systems

Engineering Symptoms of Civilization The Onset of Civilization The Pinnacle of Civilization

An Important Innovation Development of Reactors

CVs for Day to Day Use Supply & Use of LPG through Cylinders

Domestic Using of LPG

Control Mass or Control Volume A Representation for Engineering Convenience

CM & CV Representation of a Device Control Mass representation of Can: The total Deodorant Control Volume representation of Can: Deodorant in side the can At time t = 0, (before spray). The total mass of Deodorant =Mass of Deodorant in side the can Control mass is same as control volume

CM & CV Representation of a Device At t =  t (after spraying) Control mass = control volume + spray It is possible to relate CM and CV of a device at any instant! Principle of Conservation mass says that the rate of change of mass for a control mass is always zero. What about control volume?

The Thermodynamic Control Volume In real engineering devices, we are usually interested in a region of space, i.e, control volume and not particular control mass. The laws of nature are connected to Control Mass. Therefore, we need to transform Laws of Conservation for a control mass to a control volume. This is accomplished through the use of Reynolds Transport Theorem. Specially derived in thermodynamics for CV.

Flowing Fluid Through A CV A typical control volume for flow in an funnel-shaped pipe is bounded by the pipe wall and the broken lines. At time t 0, all the fluid (control mass) is inside the control volume.

The fluid that was in the control volume at time t 0 will be seen at time t 0 +  t as:.

The control volume at time t 0 +  t. There will be differences between the fluid (control mass) and the control volume at time t 0 +  t. The control mass at time t 0 +  t.

I II Consider a control mass and a control volume (C.V.) as follows: the control mass occupies region I and C.V. (region II) at time t 0. Fluid particles of region – I are trying to enter C.V. (II) at time t 0. II III the same control mass occupies regions (II+III) at t 0 +  t Fluid particles of I will enter CV-II in a time  t. Few more fluid particles which belong to CV – II at t 0 will occupy III at time t 0 +  t. A Generalized Functional Model for CV

The control volume may move as time passes. I II At time t 0 II III At time t 0 +  t I is trying to enter CV at time t 0 III has left CV at time t 0 +  t Reynolds' Transport Theorem

For and infinitesimal time duration The rate of change of property B of the system. The above mentioned change has occurred over a time  t, therefore Time averaged change in any general property of a control mass, B CM is A Simple Accounting !!!

Conservation of Mass Let B = mass of the system, m. The rate of change of mass in a control mass should be zero.

Conservation of Momentum Let B = momentum of the system, mV. The rate of change of momentum for a control mass should be equal to resultant external force.

First Law of Thermodynamics Let B = E, Energy of the system, me. The rate of change of energy of a control mass should be equal to difference of work and heat transfer rates.

Rate Equations for Laws of Nature : Control Mass Conservation of Mass : Conservation of Momentum : First law of thermodynamics :

First Law for A Control Volume Conservation of mass: Conservation of energy: Conservation of momentum:

More Mathematical Definitions for A CV

Thermodynamic Nature of Variables of CV Incoming and outgoing mass flow rates are steady. Properties of incoming and outgoing flows are homogeneous and invariant. Properties of CV can be inhomogeneous and variant. Following features for CV are possible. Inhomogeneous and variant : Difficult to solve using thermodynamics. Homogeneous and invariant : A trivial situation for a CV. No heat or work interactions required. Inhomogeneous and invariant: Steady State System. Rate of work and heat interactions must be invariant too. Homogeneous and variant: Transient System. Rate of work and heat interactions are variant.

Applications of CV Analysis A means to estimate the size of engineering devices.

First Law for CV:Steady State Steady Flow Conservation of mass: Conservation of energy: Properties of CV are Invariant: NO accumulation or depletion of mass of a CV. NO addition or removal of energy for a CV.

Rate of Work and Heat Transfers : SSSF Both rate of heat transfer and rate of work transfer are invariant. The work done per unit mass and heat transfer per unit mass are invariant. The specific work transfer at various parts of a CV can be different. The specific heat transfer at various parts of a CV can be different. Let :

The Steam Power Plant Executes a Thermodynamic Cycle using an assembly of CVs

Complex Engineering Control Volume : SSSF SSSF: Conservation of mass First Law :

Comparison of A control mass and SSSF CV during a change of state Consider compression processes using CM and CV devices. Reciprocating compressor : A Control Mass : m CM Initial State : p 1,v 1 and T 1. Final State : p 2,v 2 and T 2.

Centrifugal compressor : A Control Inlet State : p in,v in and T in. Outlet State : p out,v out and T out. Various parts of A CV are at different states during SSSF process !!

Salient Features of Process Rate of mass inflow = Rate mass outflow. Work done per unit mass is invariant. Heat transfer per unit mass is invariant. Change of state or process is not for the CV! The incoming fluid changes its state from inlet to exit conditions. A CM possesses different states at different time intervals. A CV possesses All states at any time but at different spatial locations. A CV with SSSF process is an inhomogeneous device. A CV can work continuously without changing its state. A CV lowers the importance of time !