Closed Systems

Closed systems (control mass) are thermodynamic systems in which a fixed amount of mass is considered; no mass crosses the system boundary, but energy in the form of heat and work may cross. The system energy E includes internal energy (U), macroscopic kinetic energy (KE) and potential energy (PE). For engineering problems with closed systems we often assume constant specific heats for ideal gases or quasi‑equilibrium (reversible) processes when integrating boundary work. Common processes: isochoric (constant volume, Wb = 0), isothermal (ΔU ≈ 0 for ideal gas), adiabatic (Q = 0), and reversible adiabatic (isentropic) where PV^γ = const for ideal gases.

Governing FormulaKey relations for closed systems (SI units): - First law (control mass): ΔE = Q - W, where ΔE = ΔU + ΔKE + ΔPE (J), Q is heat added to system (J), W is work done by system (J). - Internal energy change for ideal gas (constant cv): ΔU = m cv (T2 - T1) (J). - Boundary (PdV) work (quasi‑static): Wb = ∫_{V1}^{V2} P dV. For reversible ideal gas processes: - Isothermal (T const): W = m R T ln(V2/V1) (J) (R is specific gas constant, J·kg^{-1}·K^{-1}). - Adiabatic reversible (Q = 0, PV^γ = const): T2 = T1 (V1/V2)^{γ-1} and W = (P2V2 - P1V1)/(1 - γ). - Polytropic process (P V^n = const, n ≠ 1): W = (P2V2 - P1V1)/(1 - n). - Rigid/isochoric process: V = const → Wb = 0. (Assume sign convention: W > 0 when work is done by the system.)

Knowledge Check

10 Questions

1.Which statement correctly defines a closed system (control mass)?

2.Which is the correct statement of the first law of thermodynamics for a closed system (sign convention: W > 0 is work done by the system)?

3.For a reversible isothermal process of an ideal gas in a closed system (temperature T constant), which expression gives the boundary work W (J)? (m = mass, R = specific gas constant, V1 and V2 are initial and final volumes)

4.A closed rigid vessel (mass m = 0.02 kg of air) is heated from 300 K to 600 K at constant volume. Assume air is an ideal gas with cv = 718 J·kg^{-1}·K^{-1}. What is the heat transfer Q (J) to the air? (Boundary work = 0.)

5.Air (ideal gas, γ = 1.4) in a closed piston is compressed reversibly and adiabatically from V1 = 0.100 m3 and T1 = 300 K to V2 = 0.020 m3. What is the final temperature T2 (K)?

6.A closed system undergoes a reversible adiabatic process (Q = 0). The system mass is m = 0.5 kg; cv = 718 J·kg^{-1}·K^{-1}. Temperature rises from 300 K to 600 K. What is the work W (J) done by the system? (Sign convention: W > 0 = work done by system.)

7.A closed system undergoes a polytropic compression with n = 1.2. Given P1 = 100 kPa, V1 = 0.010 m3 and V2 = 0.005 m3, compute the boundary work W (J) = ∫P dV (use SI units).

8.Which terms are included when writing the total energy E of a closed system for mechanical/thermal analyses (neglecting chemical/electrical energies)?

9.A closed system is confined in a rigid vessel (V = constant). What is the boundary (PdV) work done by the system for any process in this vessel?

10.A closed system undergoes a process with ΔU = +5000 J, ΔKE = -200 J, ΔPE = 0, and the system performs W = 1200 J of work on the surroundings (W > 0 means work done by system). What is the heat transfer Q (J) to the system?