First Law 
A statement of the conservation of energy in a thermodynamic system.
Net energy crossing a system boundary equals the energy change
inside the system. Heat (Q) is energy transferred due to a temperature
difference and is considered positive if it is inward or added to the
system. 
Closed Thermodynamic System 
DU = Q  W DU = change in system internal energy Q = net heat crossing boundary (Q is positive if heat added to system) W = net work done by or on the system (W is positive if the system does work) 
Closed System Special Cases 

Processes 
For detailed P,V,T , work, Q, Enthalpy, relationships for all processes, click
here 
Constant Pressure 
Charles' Law T/v = constant for an ideal gas when pressure is constant W = PDV 
Constant Volume 
T/P = constant for an ideal gas when volume is constant W = 0 
Constant Temp. 
Doyle's Law PV = constant for an ideal gas when temperature is constant w = R'T ln(v_{2}/v_{1}) = R'T ln(P_{1}/P_{2}) R' = R/Mwt 
Isentropic 
PV^{k} = constant for an ideal gas w = (P_{2}v_{2}  P_{1}v_{1})/(1  k) w = R'(T_{2}  T_{1})/(1  k) 
Polytropic 
PV^{n} = constant for an ideal gas w = (P_{2}v_{2}  P_{1}v_{1})/(1  n) w = R'(T_{2}  T_{1})/(1  n) 
Open Thermodynamic System 
Mass can cross system boundary (flow). Includes flow work of mass entering system. Kinetic and Potential energies usually neglected. Reversible work: 
First Law (Energy Balance) 
(In  Out) = Change Sm'_{i}[h_{i}+V_{i}^{2}/2a + gZ_{i} ]  Sm'_{e}[h_{e}+V_{e}^{2}/2a + gZ_{e} ] + Q'_{in}  W'_{net} = d(m_{s}u_{s})dt m'_{i} = mass flow rate in. h_{i} = enthalpy of mass in. V_{i} = Velocity of mass in. Z_{i} = elevation of mass in. m'_{e} = mass flow rate exit. h_{e} = enthalpy of mass exit. V_{e} = Velocity of mass exit. Z_{e} = elevation of mass exit. Q'_{in}= rate of heat transfer W'_{net} = rate of net or shaft work transfer m_{s} = mass of fluid with in system u_{s} = specific internal energy of system a = kinetic energy correction factor a = 1 for turbulent flow a = 0.5 for laminar flow 
Special Cases of Open Systems 

Constant Volume 
w = v(P_{2}  P_{1}) 
Constant Pressure 
w = 0 
Constant Temp 
Pv = constant for ideal gas w = R'T ln(v_{2}/v_{1}) = R'T ln(P_{1}/P_{2}) R' = R/Mwt 
Isentropic 
PV^{k} = constant for an ideal gas w = k(P_{2}v_{2}  P_{1}v_{1})/(1  k) w = kR'(T_{2}  T_{1})/(1  k) W_{is} = [ kR'T_{1} / (k1) ] [1  (P_{2}/P_{1})^{[(k1)/k]} ] 
Polytropic 
w = n(P_{2}v_{2}  P_{1}v_{1})/(1 
n) 
Steady State Systems 
The state of the system does not change with time. 
Energy Balance 
(In  Out) = 0 Sm'_{i}[h_{i}+V_{i}^{2}/2a + gZ_{i} ]  Sm'_{e}[h_{e}+V_{e}^{2}/2a + gZ_{e} ] + Q'_{in}  W'_{net} = 0 Sm'_{i} = Sm'_{e} Q' = rate of heat transfer W' = rate of work transfer 
Special Cases Of Steady Flow Energy Equation 

Nozzles/Diffusers 
Assumptions: Velocity term is significant No elevation change No heat transfer, Q = 0 No work Single mass stream h_{i}+V_{i}^{2}/2 = h_{e}+V_{e}^{2}/2 efficiency = (V_{e}^{2}V_{i}^{2})/[2(h_{i}  h_{es})] h_{es}= enthalpy at isentropic exit state 
Turbines, Pumps, Compressors 
Assumptions: Adiabatic  no heat transfer, Q= 0 Velocity terms ignored. Work is significant Single mass stream h_{i} = h_{e}+ w Efficiency (turbine)= (h_{1}  h_{e})/(h_{i}  h_{es}) Efficiency (comp, pump)= (h_{es}  h_{i})/(h_{e}  h_{i}) 
Throttling Valve Throttling Process 
Assumptions: W = 0 Q = 0 Single mass stream Velocity terms often insignificant h_{i} = h_{e} 
Boilers, Condensers, Evaporators, one side of a Heat Exchanger 
Assumptions: Heat transfer terms are significant Single mass stream h_{i} + q = h_{e} 
Heat Exchangers 
Assumptions: Q = 0 W = 0 Two mass streams (m'_{1}, m'_{2}) m'_{1}(h_{1i}  h_{1e}) = m'_{2}(h_{2i}  h_{2e}) 
Mixers, Separators, Open or Closed Feedwater Heaters 
Sm_{i}'h_{i} = Sm'_{e}h_{e}
Sm_{i} = Sm'_{e} 
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