EIT - Engineer In Training Thermodynamics Questions and Answers — Questions and Answers
Question 1: A piston-cylinder device contains a gas that undergoes a process where 50 kJ of heat is added to the system. During this process, the gas expands and performs 20 kJ of work on the surroundings. Assuming changes in kinetic and potential energy are negligible, what is the change in the internal energy of the gas?
- 70 kJ
- 30 kJ (Correct answer)
- -30 kJ
- -70 kJ
Correct answer: 30 kJ
The First Law of Thermodynamics for a closed system is given by the equation ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. [3, 7] In this problem, Q = +50 kJ (heat is added) and W = +20 kJ (work is done by the system). Therefore, ΔU = 50 kJ - 20 kJ = 30 kJ. [9]
Question 2: A heat engine operates between a high-temperature reservoir at 800°C and a low-temperature reservoir at 100°C. What is the maximum possible thermal efficiency (Carnot efficiency) for this engine?
- 87.5%
- 29.8%
- 65.2% (Correct answer)
- 74.6%
Correct answer: 65.2%
The maximum theoretical efficiency of a heat engine is the Carnot efficiency, calculated as η_carnot = 1 - (T_L / T_H). [16, 21] The temperatures must be in an absolute scale, such as Kelvin. First, convert the Celsius temperatures to Kelvin: T_H = 800°C + 273.15 = 1073.15 K; T_L = 100°C + 273.15 = 373.15 K. [16] Then, calculate the efficiency: η_carnot = 1 - (373.15 K / 1073.15 K) ≈ 0.6523, or 65.2%.
Question 3: Air, behaving as an ideal gas with k = 1.4, undergoes a reversible and adiabatic (isentropic) compression from an initial state of 100 kPa and 300 K to a final pressure of 700 kPa. What is most nearly the final temperature?
- 522 K (Correct answer)
- 172 K
- 2100 K
- 455 K
Correct answer: 522 K
For an isentropic process of an ideal gas, the relationship between temperature and pressure is given by T₂/T₁ = (P₂/P₁)^((k-1)/k). [8, 13] First, calculate the exponent: (k-1)/k = (1.4-1)/1.4 = 0.4/1.4 ≈ 0.2857. Now, solve for T₂: T₂ = T₁ * (P₂/P₁)^((k-1)/k) = 300 K * (700 kPa / 100 kPa)^(0.2857) = 300 K * (7)^(0.2857) ≈ 300 K * 1.74 = 522 K.
Question 4: A rigid 0.5 m³ tank contains a saturated liquid-vapor mixture of water at 150 kPa. If the mass of the saturated liquid is 1.2 kg and the mass of the saturated vapor is 0.8 kg, what is the quality (x) of the mixture?
- 0.60
- 0.67
- 0.40 (Correct answer)
- The quality cannot be determined without volume data.
Correct answer: 0.40
The quality (x) of a saturated liquid-vapor mixture is defined as the ratio of the mass of the vapor to the total mass of the mixture. The total mass (m_total) is the sum of the liquid mass (m_f) and the vapor mass (m_g). m_total = 1.2 kg + 0.8 kg = 2.0 kg. The quality is x = m_g / m_total = 0.8 kg / 2.0 kg = 0.40. The volume and pressure data are not needed for this specific calculation.
Question 5: Which of the following describes the process occurring in the turbine of an ideal Rankine cycle?
- Isentropic expansion (Correct answer)
- Isobaric heat addition
- Isentropic compression
- Isobaric heat rejection
Correct answer: Isentropic expansion
The ideal Rankine cycle consists of four processes: 1) Isentropic compression in the pump, 2) Isobaric (constant pressure) heat addition in the boiler, 3) Isentropic expansion in the turbine, and 4) Isobaric (constant pressure) heat rejection in the condenser. [1, 2, 4] Therefore, the process in the turbine is an isentropic expansion.
Question 6: A flat wall is 0.2 m thick and has a thermal conductivity of 1.5 W/m·K. If the wall's inner surface is at 100°C and its outer surface is at 40°C, what is the rate of heat transfer per unit area (heat flux) through the wall under steady-state conditions?
- 1800 W/m²
- 12 W/m²
- 300 W/m²
- 450 W/m² (Correct answer)
Correct answer: 450 W/m²
The rate of steady-state heat conduction through a plane wall is described by Fourier's Law of Heat Conduction: q = -k * (dT/dx). [5] For a flat wall with constant temperatures, this simplifies to q = k * (T_hot - T_cold) / L, where q is the heat flux (W/m²), k is the thermal conductivity, T is temperature, and L is the thickness. q = 1.5 W/m·K * (100°C - 40°C) / 0.2 m = 1.5 * (60) / 0.2 = 450 W/m². Note that a temperature difference in Celsius is equal to a temperature difference in Kelvin.
EIT - Engineer In Training Thermodynamics Questions and Answers
A piston-cylinder device contains a gas that undergoes a process where 50 kJ of heat is added to the system.
During this process, the gas expands and performs 20 kJ of work on the surroundings.
Assuming changes in kinetic and potential energy are negligible, what is the change in the internal energy of the gas?