--- title: "Nitrogen piston with stops: work and heat" subject: "Fundamental of Thermodynamics & Heat Transfer" chapter: 4 key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:nitrogen-piston-stops-0-2mpa-70c" source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/nitrogen-piston-stops-0-2mpa-70c site: BCT Engineering --- # Nitrogen piston with stops: work and heat Fundamental of Thermodynamics & Heat Transfer · Chapter 4: First Law of Thermodynamics - Asked in: 2071 Magh, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/nitrogen-piston-stops-0-2mpa-70c - Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-4 ## Question Nitrogen (0.10 kg) in the piston-cylinder device shown in Figure P.3 has an initial pressure of 0.2 MPa and temperature of 70°C. Energy is added until the piston just reaches the upper stops where the total volume is 0.015 m³. It takes a pressure of 0.4 MPa to move the piston. Calculate the total work done and heat transfer. [R = 297 J/kg.K, Cv = 743 J/kg.K] [Figure P.3: cylinder containing N2 with a piston and upper stops.] ## Short answer Heating at constant volume to 400 kPa, then constant-pressure expansion to 0.15 m³. Work W = 39.6 kJ, heat transfer Q = 164.2 kJ. ## Answer **Given:** m = 0.10 kg N₂, R = 0.297, c_v = 0.743 kJ/kg·K; P₁ = 0.2 MPa = 200 kPa, T₁ = 70 °C = 343.15 K; upper stops at V_total = 0.015 m³ (as printed); 0.4 MPa (400 kPa) is needed to move the piston. **Check of data:** V₁ = mRT₁/P₁ = 0.1 × 0.297 × 343.15/200 = 0.0510 m³. This is larger than the printed 0.015 m³, so the data are inconsistent: the stop volume is evidently 0.15 m³ (or the mass is 0.010 kg). The solution below uses **m = 0.10 kg and V_stops = 0.15 m³**. **Process:** 1. 1 → 2: the piston rests on the lower stops, so heating is at constant volume V = 0.0510 m³ until P = 400 kPa: T₂ = T₁ × 400/200 = 686.3 K 2. 2 → 3: the piston moves at constant P = 400 kPa until it reaches the upper stops, V₃ = 0.15 m³: T₃ = P₃V₃/(mR) = 400 × 0.15/(0.1 × 0.297) = 2020 K ```text P (kPa) 400 | 2------------3 | | | | 1-2: constant V 200 | 1 +------------------- v 0.051 0.15 ``` **Work** (only in 2 → 3): W = P (V₃ − V₂) = 400 × (0.15 − 0.0510) = **39.6 kJ** **Heat:** ΔU = m c_v (T₃ − T₁) = 0.1 × 0.743 × (2020 − 343.15) = 124.6 kJ Q = ΔU + W = 124.6 + 39.6 = **164.2 kJ** **Answer: W ≈ 39.6 kJ; Q ≈ 164 kJ.** (If instead m = 0.010 kg with V = 0.015 m³ is meant, every quantity is one tenth: W = 3.96 kJ, Q = 16.4 kJ.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. V1 = mRT1/P1 = 0.051 m³ exceeds the printed 0.015 m³, so: A. The data are inconsistent; the solution uses V_stops = 0.15 m³ B. The answer is impossible C. Use 0.015 m³ anyway D. Gas is not ideal Answer: A. A note in the answer corrects the data. (Key point: Data check) 2. Initial heating is: A. Constant pressure first B. Constant volume until 400 kPa, then constant pressure to the stops C. Isothermal D. Adiabatic Answer: B. Piston needs 0.4 MPa to move. (Key point: Process) ## Related in Fundamental of Thermodynamics & Heat Transfer - [Nitrogen in piston cylinder: work and heat](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Anitrogen-piston-work-heat) — Fundamental of Thermodynamics & Heat Transfer, chapter 4 - [Piston cylinder with stops: 2 kg H2O to 250°C](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Awater-80c-0-05m3-400kpa-250c-work) — Fundamental of Thermodynamics & Heat Transfer, chapter 3 - [Argon in piston cylinder with stops: work](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aargon-piston-6mpa-200c-to-8mpa-800c) — Fundamental of Thermodynamics & Heat Transfer, chapter 3 - [Water in piston cylinder with stops, 200 kPa](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Awater-piston-stops-200kpa-50c) — Fundamental of Thermodynamics & Heat Transfer, chapter 3 - [Piston cylinder 400 L to 600 L: work and heat](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Apiston-cylinder-400l-600l-work-heat) — Fundamental of Thermodynamics & Heat Transfer, chapter 3 - [Piston cylinder: 2 kg water 500 kPa, 20% quality](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Asteam-piston-500kpa-quality-20) — Fundamental of Thermodynamics & Heat Transfer, chapter 3