05first_law

# 05first_law - Sept 2005: changes reflect text: Woud Sept...

This preview shows pages 1–4. Sign up to view the full content.

First Law Sept 2005: changes reflect text: Woud Sept 2006: added examples first law: during any cycle a system undergoes, the cyclic integral of the heat is proportional to the cyclic integral of the work pg 83 van Wylen & Sonntag Fundamentals of Classical Thermodynamics 3rd Edition SI Version first law for cycle 1 dQ = 1 dW (5.2) The net energy interaction between a system and its environment is zero for a cycle executed by the system. pg 2 Cravalho and Smith 1 dQ 1 dW = 0 where integral are cyclic and dQ = δ Q dW = δ W plot data Pressure Volume plot for Processes 0.5 1 1.5 2 2.5 p 1 2 1 0.5 1 1.5 2 2.5 v A process B process 1 2 2 2 2 C process 2 1 2 1 2 2 1 dQ = 1 dW apply first law to cycle A B 1 dQ A 1 dQ B 1 dW A 1 dW B + + = 2 1 2 1 1 1 2 1 apply first law to cycle A C 1 dQ A 1 dQ C 1 dW A 1 dW C + + = 1 1 subtract A C from A B 1 dQ B 1 dQ C 1 dW B 1 dW C = rearrange . .. 1 i.e. δ Q - δ W is a point function . .. only dependent 2 9/21/2006 1 9/21/2006 dE δ Q 1 dQ_W B 1 dQ_W C = upon the end points => define as . .. energy, point function − δ W = 2 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
first law for system (Woud: Closed system) - change of state N.B. Woud starts with rate equation and obtains this assuming steady state rearrange and integrate . .. Q 1_2 is the heat transferred TO system = + δ Qd E + δ W Q 1_2 = E 2 E 1 W 1_2 E 1 E 2 are intial and final values of energy of system and . .. (5.5) W 1_2 is work done BY the system energy E consists of internal energy + kinetic energy + potential energy E = U + K + PE dE = dU + dKE + dPE and first law can be restated . .. δ + dU + dPE + (5.4) = δ W = + dKE δ W Closed System d U = Q_dot W_dot dU = δ Q − δ W m_dot e = m_dot i = 0 (W 2.3) dt d and δ : VW&S: page 62 Woud page 11 d = differential of point functions state variables difference between d and δ δ = differential of path functions - amount depends on path/process: diminutive see discussion of cyclic process below cycle may be considered a closed system; initial state and final state are identical, For example (detailed discussion later) set up limits and calculations p-v plot of Brayton cycle 0 1 2 3 4 5 0 2 4 6 pressure volume adiabatic compression heat addition adiabatic expansion in turbine heat rejection closed (cycle) t d U d = 0 Q_dot W_dot = Q_dot = W_dot Q cycle W cycle = (W 2.6) this is where we started above using different approach to first law 9/21/2006 2 9/21/2006
example 5.3 Sonntag example 5.3: vessel with volume 5 m 3 contains 0.05 m 3 of saturated liquid water and 4.95 m 3 of saturated water vapor at 0.01 MPa. Heat is added until the vessel is filled with saturated vapor. Determine Q. State 1: V := 5m 3 V := 4.95m 3 MPa := 10 6 Pa 3 vap kJ := 10 J 3 V liq := 0.05m p := 0.1MPa 3 m kJ constant volume and := 0.001043 := 417.36 page 616 1 Q 2 mass => constant v v f kg u f kg Sonntag steam tables at p = m 3 kJ kJ 0.1 MPa v g := 1.694 u g := 2506.1 u fg := 2088.7 kg kg kg State 2: V 2 = V v = v g u = u g Liq H 2 O Vap H 2 O first law: Q 1_2 = E 2 E 1 + W 1_2 W 1_2 = 0 Q 1_2 = U 2 U

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 05first_law - Sept 2005: changes reflect text: Woud Sept...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online