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Note for Basics of Mechanical Engineering - BME by Yash Yadav

  • Basics of Mechanical Engineering - BME
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www.vidyarthiplus.com Chapter 3 THE FIRST LAW OF THERMODYNAMICS Energy interactions between a system and its surroundings across the boundary in the form of heat and work have been discussed separately in the previous chapter. So far, no attempt has been made to relate these interactions between themselves and with the energy content of the system. First law of thermodynamics, often called as law of conservation of energy, relating work, heat, and energy content of the system will be discussed in detail in this chapter. 3.1 First Law of Thermodynamics In its more general form, the first law may be stated as follows “When energy is either transferred or transformed, the final total energy present in all forms must precisely equal the original total energy”. It is based on the experimental observations and can not be proved mathematically. All the observations made so far, confirm the correctness of this law. 3.2 First Law of Thermodynamics for a Closed System Undergoing a Process First law can be written for a closed system in an equation form as  Energy entered into the system    Energy left  Change in the energy   +  the system  = content of the system      For a system of constant mass, energy can enter or leave the system only in two forms namely work and heat. Let a closed system of initial energy E1 receives Q units of net heat and gives out W units of work during a process. If E2 is energy content at the end of the process as given in Figure 3.1, applying first law we get Thermodynamics I [MIME3110] 22 www.vidyarthiplus.com

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www.vidyarthiplus.com Q − W = (E2 − E1) ...(3.1) Where the total energy content Ε = Internal Energy = U + + Kinetic energy + 1 mC 2 2 gc + Potential energy mgz The term internal energy usually denoted by the letter U is the energy due to such factors as electron spin and vibrations, molecular motion and chemical bond. Kinetic energy term is due to the system movement with a velocity C. For stationary systems this term will be zero. The term gc is a constant of value 1 in SI unit. It will be dropped here after since SI unit is followed throughout the book. Potential energy term is due to the location of the system in the gravitational field. It remains constant for a stationary system. The unit of energy in SI is kJ. 3.3 The Thermodynamic Property Enthalpy Consider a stationary system of fixed mass undergoing a quasi-equilibrium constant pressure process Applying first law Q12 − 1W2 = E2 − E1 where E2 − E1 = (U2 − U1) + m(C22 − C12) + mg(Z2 − Z1) = U2 − U1 since it is a stationary system. also 1W2 = p(V2 − V1) = p2V2 − p1V1 ∴ Q12 = (p2V2 − p1V1) + (U2 − U1) ∴Q12 = (U2 + p2V2) − (U1 + p1V1) The terms within brackets are all properties depending on the end states. This combination of properties may be regarded as a single property known as enthalpy. It is usually denoted by the letter H. ie H = U + pV ...(3.3a) (or) h = u + pv ...(3.3b) Thermodynamics I [MIME3110] 23 www.vidyarthiplus.com

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www.vidyarthiplus.com Where h is specific enthalpy in kJ/kg u is specific internal energy in kJ/kg and v is specific volume in m3/kg 3.4 Flow Energy Flow energy is defined as the energy required to move a mass into the a control volume against a pressure. Consider a mass of volume V entering into a control volume as given in the Figure 3.2 against a pressure p. The Flow energy = = = = = Therefore, Enthalpy = 3.5 Work done in moving the mass Force × distance pA × dx p × (Adx) pV Internal energy + Flow energy ...(3.4) First Law of Thermodynamics for a Control Volume Mass simultaneously entering and leaving the system is a very common phenomenon in most of the engineering applications. Control volume concept is applied to these devices by assuming suitable control surfaces. To analyze these control volume problems, conservation of mass and energy concepts are to be simultaneously considered. Energy may cross the control surface not only in the form of heat and work but also by total energy associated with the mass crossing the boundaries. Hence apart from kinetic, potential and internal energies, flow energy should also be taken into account. Thermodynamics I [MIME3110] 24 www.vidyarthiplus.com

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www.vidyarthiplus.com Conservation of mass Total mass  Total mass   Net change in the  entering the  + leaving the  = mass content of the       control volume control volume control volume  Conservation of energy  Net energy crossing the Total energy  Total energy   Net change  boundary in the  associated withthe  associated withthe   in theenrgy   +   − =   form of heat  mass entering  mass leaving  content of the           and work  the control volume the control volume control volume . W . min ...(3.5) Control Volume . mout . Q Control Surface Figure 3.3 First Law of Thermodynamics Applied to a control Volume As a rate equation, it becomes [Q& − W& ]+ ∑ m in 3.6     C2 C2 h + + Zg − m h + + Zg  = [∆ECV ] in   ∑ out  2 2   out   ...(3.6) The Steady-state Flow Process When a flow process is satisfying the following conditions, it is known as a steady flow process. 1. The mass and energy content of the control volume remains constant with time. 2. The state and energy of the fluid at inlet, at the exit and at every point within the control volume are time independent. 3. The rate of energy transfer in the form of work and heat across the control surface is constant with time. Thermodynamics I [MIME3110] 25 www.vidyarthiplus.com

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