Open Systems

Open systems (control volumes) are thermodynamic systems through which mass and energy can cross the system boundaries. Analysis of open systems uses conservation of mass and the first law for control volumes (steady- or unsteady-flow energy equation). Key concepts include mass flow rate (m_dot), specific enthalpy (h = u + p·v), flow work (p·v), kinetic and potential energy terms, and steady-flow devices such as nozzles, diffusers, turbines, compressors, throttling valves, mixers, and heat exchangers. Sign conventions: Q_dot is heat added to the control volume; W_dot is shaft work done by the control volume. For steady operation, control-volume internal energy storage does not change with time.

Governing FormulaContinuity (single inlet/outlet): m_dot_in = m_dot_out (steady state). General steady-flow energy equation (neglecting potential energy): Q_dot - W_dot = m_dot [ (h2 - h1) + (V2^2 - V1^2)/2 ]. Specific enthalpy: h = u + p·v. Flow work (specific): p·v (= p/ρ). Stagnation (total) enthalpy: h0 = h + V^2/2 (neglecting potential). For ideal gases (constant cp): h = cp·T and for isentropic ideal-gas compression/expansion: T2/T1 = (p2/p1)^{(γ-1)/γ}. Heat transfer for a stream: Q_dot = m_dot·cp·(T_in - T_out) (steady, no phase change, constant cp).

Knowledge Check

10 Questions

1.Which statement correctly defines an open system (control volume) in thermodynamics?

2.Which expression is the correct steady-flow energy equation for a control volume (neglect potential energy) between inlet 1 and outlet 2, with Q_dot heat added and W_dot shaft work done by the system?

3.What is the specific flow work (per unit mass) required to push fluid into a control volume?

4.Air (ideal gas) flows through an isentropic, adiabatic nozzle from state 1 (p1 = 400 kPa, T1 = 500 K) to state 2 (p2 = 100 kPa). Inlet velocity is negligible. Use cp = 1005 J·kg^-1·K^-1 and γ = 1.4. Neglect potential energy. What is the approximate exit velocity V2 (m·s^-1)?

5.A steady compressor increases the temperature of air from 300 K to 600 K. Mass flow is 0.50 kg·s^-1. Assume adiabatic, negligible kinetic/potential energy changes and cp = 1005 J·kg^-1·K^-1. What is the required compressor power (magnitude of shaft work input) in kW?

6.Two air streams mix adiabatically in a steady mixer. Stream 1: m_dot1 = 2.0 kg·s^-1 at 400 K. Stream 2: m_dot2 = 3.0 kg·s^-1 at 300 K. Specific heats are identical (cp cancel). What is the outlet temperature T_out (K)?

7.The stagnation (total) enthalpy per unit mass h0 in a steady-flow device (neglecting potential energy) is defined as:

8.In a steady control volume there are two inlet streams with mass flow rates m_dot1 = 1.20 kg·s^-1 and m_dot2 = 0.80 kg·s^-1 and one outlet stream m_dot3. Assuming steady mass balance and no accumulation, what is m_dot3 (kg·s^-1)?

9.A hot fluid stream (m_dot_h = 1.00 kg·s^-1) enters a heat exchanger at 500 K and leaves at 350 K. For the hot stream cp = 1005 J·kg^-1·K^-1. What is the rate of heat released by the hot stream Q_dot (kW)? Assume steady operation and no phase change.

10.During a steady throttling (Joule–Thomson) process through a valve (adiabatic, negligible kinetic/potential energy, no shaft work), which thermodynamic property is conserved across the valve for any fluid?