Question

A thermally insulated, closed copper vessel contains water at 15°C. When the vessel is shaken vigorously for 15 minutes, the temperature rises to 17°C. The mass of the vessel is 100g and that of the water is 200g. The specific heat capacities of copper and water are 420J/kg-K and 4200J/kg-K respectively. Neglect any thermal expansion, (a) How much heat is transferred to the liquid—vessel system ? (b) How much work has been done on this system ? (c) How much is the increase in internal energy of the system?

Answer 1

t₁ = 15°c t₂ = 17°c 

Δt = t₂ – t₁ = 17 – 15 = 2°C = 2 + 273 = 275 K

m_v = 100g = 0.1kg 

m_w = 200g = 0.2kg 

cu_g = 420J/kg–k 

W_g = 4200J/kg–k 

(a) The heat transferred to the liquid vessel system is 0. The internal heat is shared in between the vessel and water. 

(b) Work done on the system = Heat produced unit => dw = 100 × 10^–3 × 420 × 2 + 200 × 10^–3 × 4200 × 2 = 84 + 84 × 20 = 84 × 21 = 1764J. 

(c) dQ = 0, dU = – dw = 1764. [since dw = –ve work done on the system]