Chemistry - Thermodynamics - I Question with Solution | TestHub
The vapour pressure of water at 343 K is 234 mm Hg. The external pressure on H₂O (l) taken in a cylinder fitted with a frictionless movable piston initially containing 1.8 L (= 1.8 kg) of H₂O (l) at 343 K is increased to 1 atm at constant temperature. Then heat is supplied keeping the pressure constant till 0.9 L of H₂O (l) is evaporated to form H₂O (g) at 373 K. Assume the internal energy of the liquid to be dependent only on temperature. Answer the following questions by carefully observing the diagrams and the data provided. Given:
Specific heat of H₂O (l) = 4.2 J/°C-g
ΔHvap at 373 K and 1 atm = +40 kJ/mol
1 L-atm = 100 J
R = 8 J/K-mol
Total change in ΔU (in kJ) going from State 1 to State 3 is
Options:
Answer:
Solution:
State 1 → 2: ΔU = 0. State 2 → 3 (P = 1 atm constant): heat 1.8 kg of liquid from 343 K to 373 K, q₁ = 1800 × 4.2 × 30 = 226.8 kJ; evaporate 0.9 kg, n = 900/18 = 50 mol, q₂ = 50 × 40 = 2000 kJ. qp = ΔH = 2226.8 kJ. w = −PΔV = −nRT = −50 × 8 × 373 = −149.2 kJ. ΔU = 2226.8 − 149.2 = 2077.6 kJ. Matches (a).
