Mechanical Engineering - MCQ Practice Questions

The Carnot efficiency is the maximum theoretical efficiency for any heat engine, given by η = 1 - (T_C/T_H), where temperatures are in Kelvin.

Throttling is an isenthalpic process where enthalpy remains constant (H_initial = H_final) as the fluid expands through a restriction.

Exergy is maximum work available from a system. At dead state (T₀, P₀, same as surroundings), exergy is zero as no useful work can be extracted.

Compressibility factor Z = PV/(nRT). For ideal gas, Z = 1. For real gases, Z ≠ 1 due to molecular interactions.

When n = 0, PV⁰ = P = constant, which is an isobaric process. When n = 1 (isothermal), n = γ (adiabatic), n = ∞ (isochoric).

First Law: ΔE_system = Q - W, where Q is heat added to system and W is work done by system. This is the IUPAC convention.

For an irreversible process in an isolated system, total entropy increases (ΔS_total > 0). Heat transfer between bodies at different temperatures is irreversible.

For a monatomic ideal gas with 3 translational degrees of freedom: Cv = ($\frac{3}{2}$)R. For diatomic: ($\frac{5}{2}$)R; for polyatomic: ($\frac{7}{2}$)R.

The throttling process is isenthalpic (constant enthalpy). The enthalpy remains the same before and after the expansion valve.

Q = m × L_fg = 0.5 kg × 1941 kJ/kg = 970.5 kJ heat is removed during condensation

In an ideal Rankine cycle, turbine expansion is isentropic (reversible and adiabatic), maximizing work output. Real turbines follow this closely but with some irreversibilities.

The second law states that entropy of an isolated system must increase or remain constant (reversible). A decrease in total entropy violates the second law and is impossible.

u = u_f + x × u_fg, so x = (u - u_f)/u_fg = (2400 - 1317.3)/1753.7 = 1082.$\frac{7}{1753}$.7 ≈ 0.62

For polytropic process with n=1: PV = constant, which is the ideal gas law at constant temperature, making it isothermal (T = constant).

Otto cycle efficiency = 1 - (1/r^(γ-1)) = 1 - ($\frac{1}{10}$^0.4) = 1 - ($\frac{1}{2}$.512) = 1 - 0.3981 = 0.602 ≈ 60.2%

During phase transitions (like vaporization at constant T and P), infinite heat can be absorbed without temperature change, making C_p → ∞.

Efficiency η = W/Q_in = (Q_in - Q_out)/Q_in = (2000-1200)/2000 = $\frac{800}{2000}$ = 0.4 = 40%. Work output W = 800 J

Maximum efficiency occurs in a Carnot engine: η = 1 - (T_cold/T_hot) = 1 - ($\frac{300}{500}$) = 1 - 0.6 = 0.4 or 40%

The first law states that dU = Q - W, where heat (Q) and work (W) are energy transfer mechanisms, not state properties. Internal energy (U) is a state property.

In adiabatic process, Q = 0. From first law: dU = -W. During expansion, W > 0, so dU < 0, meaning internal energy and temperature decrease.