3(2).pdf Thermodynamics PDF

Work Done for Closed System or Non-Flow Process Generalized Equation In a closed system or non-flow process, work is done on or by the system without any mass entering or leaving the system. F= PA, where P is the pressure A is the area of the piston face  First Law Applied to Different...

Work Done for Closed System or Non-Flow Process Generalized Equation In a closed system or non-flow process, work is done on or by the system without any mass entering or leaving the system. F= PA, where P is the pressure A is the area of the piston face  First Law Applied to Different Processes 1. Isochoric Process or Constant Volume Process: A volume change is zero, so the work done is zero. Volume of the system = Constant Change in volume = 0 If, change in volume = 0, then work done is zero. According to the 1st law of thermodynamic law Q = W + dU If W = 0 Q = dU = mCv(T2-T1) 2. Constant Pressure or Isobaric Process: The pressure remains constant during this process. So, W = P∆V P(V2−V1) W = P(V2−V1) According to thermodynamic 1st law of thermodynamics Q = dU + W Q = P(V2−V1) + dU Note: If volume increases, work done is positive, else negative. 3. Constant Temperature or Isothermal Process: It is a thermodynamic process in which temperature remains constant. We know, W=∫PdV According to Ideal Gas equation, PV = mRT = C PV = C C P= V P1V1 = P2V2 = C W=∫PdV 𝑉2 𝑉2 W = mRT ln = P1V1 ln 𝑉1 𝑉1 Key Points W = +ve (VB > VA) W = -ve (VA > VB) dU = 0 Internal energy only depends on temperature If temperature = Constant Internal Energy = Constant. According to the 1st law of thermodynamic process Q = dU + W Q=W (dU = 0) 𝑽𝟐 𝑽𝟐 Q = W = mRT ln = P1V1 ln 𝑽𝟏 𝑽𝟏 4. Adiabatic Process (No Heat Transfer): It is a thermodynamic process in which no heat is exchanged between the system and the surrounding. So, Q = 0 Mathematically this process is represented as PVγ =C γ = adiabatic index C P= Vγ P=C V -γ P1 =C V1-γ P2 =C V2-γ W=  PdV V2 W=  PdV V1 W= ( P1V1 -P2 V2 ) γ-1 According to the 1st law of thermodynamic process Q = dU + W For adiabatic Process, Q= 0 dU = -W W = - dU Note: If work done is negative internal energy increases and vice versa. Problem 1: A system undergoes three processes as shown in the figure. 1-2 is Isobaric Process, 2-3 is Adiabatic Process with ϒ =1.4 3-1 is Isothermal Process in which PV=Constant. Find the value of V2, V3, and Net Work done (Wnet) Answers V2 1.486 m3 V3 4 m3 Wnet 126 J 5. Polytropic Process: A polytropic process is a thermodynamic process in which the pressure and volume of a gas or fluid change in a way that is described by the polytropic equation. PVn = C Where n = Polytropic index 1< n < r W= ( P1V1 -P2V2 ) Polytropic Work n -1 According to the 1st law of thermodynamic process Q = dU + W dU = mCv (T2 − T1) W = mCv(T2 - T1) + ( P1V1 - P2V2 ) n -1 Note: In polytropic process there is both heat transfer and work transfer but in adiabatic process there is only work transfer. Problem 2: A system undergoes four processes as shown in the figure. 1-2 is Isothermal Process, 2-3 is Isochoric Process 3-1 is Isobaric Process 4-1 is Isochoric Process Find the Net Work done (Wnet) Problem 3: A piston–cylinder device initially contains 0.4 m3 of air at 100 kPa and 80°C. The air is now compressed to 0.1 m3 in such a way that the temperature inside the cylinder remains constant (Temperature = Constant). Determine the work done during this process.