Work done in Processes — PV diagrams, area under curve
Thermodynamics & KTG
21
JEE Qs
8%
Hard
60
min
Master the graphical interpretation of work done as area under the PV curve and diligently apply correct sign conventions for work done by/on the system.
🧮 Key Formulas
✅ Key Points for JEE
- 1Work done by a thermodynamic system is path-dependent; it depends on the specific process (path) connecting initial and final states, not just the states themselves.
- 2The area under the Pressure-Volume (P-V) curve, projected onto the volume axis, quantitatively represents the work done by the gas during the process.
- 3Work done by the gas is positive during expansion (volume increases, area on the right side of path) and negative during compression (volume decreases, area on the left side of path).
- 4For a cyclic process on a P-V diagram, the net work done by the gas is the area enclosed by the loop. A clockwise loop indicates positive net work, while an anti-clockwise loop indicates negative net work.
- 5The pressure 'P' in dW = P dV represents the *internal* pressure of the gas, which is in equilibrium with the external pressure for quasi-static processes.
⚠️ Common Mistakes
- ✕Confusing the sign convention for work done *by* the system (positive for expansion) with work done *on* the system (positive for compression).
- ✕Incorrectly calculating the area under non-linear P-V curves or for complex multi-step processes, failing to break down into simpler geometric shapes or apply integration.
- ✕Assuming work done is zero if initial and final volumes are the same, without considering the entire path (only net work in a cycle is zero for same initial/final states).
- ✕Misapplying formulas for specific processes (e.g., using W=PΔV for a non-isobaric process where P is not constant).
📝 Practice Questions
See allQ29.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, PV = constant, while in adiabatic process PVγ = constant. Here γ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below : (1) Both (A) and (R) are true and (R) is the correct (2) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true 2025 (29 Jan Shift 2) JEE Main Previous Year Paper
Q40.A cup of coffee cools from 90∘C to 80∘C in t minutes when the room temperature is 20∘C. The time taken by the similar cup of coffee to cool from 80∘C to 60∘C at the same room temperature is : (1) 13 10 t (2) 1013 t (3) 13 5 t (4) 135 t
Q42. A poly-atomic molecule ( CV = 3R, CP = 4R, where R is gas constant) goes from phase space point A (PA = 105 Pa, VA = 4 × 10−6 m3) to point B (PB = 5 × 104 Pa, VB = 6 × 10−6 m3) to point 2025 (29 Jan Shift 2) JEE Main Previous Year Paper C (PC = 104 Pa, VC = 8 × 10−6 m3). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is : (1) 500R(ln 3 + ln 4) (2) 450R(ln 4 −ln 3) (3) 500R ln 2 (4) 400R ln 4
Q29.An amount of ice of mass 10−3 kg and temperature −10∘C is transformed to vapour of temperature 110∘C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = 2100Jkg−1 K−1 , specific heat of water = 4180Jkg−1 K−1 , specific heat of steam = 1920Jkg−1 K−1 , Latent heat of ice = 3.35 × 105Jkg−1 and Latent heat of steam = 2.25 × 106 Jkg−1 ) (1) 3043 J (2) 3024 J (3) 3003 J (4) 3022 J
Q41.Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible), (1) 16 E (2) E (3) 64 E (4) 256 E
Q49.Three conductors of same length having thermal conductivity k1, k2 and k3 are connected as shown in figure. Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of θ is _______ ∘C. (Given : k1 = 60Js−1 m−1 K−1, k2 = 120Js−1 m−1 K−1, k3 = 135Js−1 m−1 K−1 ) ∣ ∣∣ 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
NCERT Chapters
- Class 11 Physics Ch 12: Thermodynamics