Given:
The system comprises of an insulated copper vessel that contains water.
t1 = 15°C, t2 = 17°C
t1 is the initial temperature of the system
t2 is the final temperature of the system
∆t = Change in the temperature of the system = t2 − t1
= 17°C − 15°C = 2°C = 275 K
Mass of the vessel, mv = 100 g = 0.1 kg
Mass of water, mw = 200 g = 0.2 kg
Specific heat capacity of copper, cu = 420 J/kg-K
Specific heat capacity of water, cw = 4200 J/kg-K
(a) Since the system is insulated from the surroundings, no heat is transferred between the system and the surroundings. This implies that the heat transferred to the liquid vessel system is zero. The internal heat is shared between the vessel and water.
(b) Work done on the system
⇒ dW = 100 × 10−3 × 420 × 2 + 200 × 10−3 × 4200 × 2
⇒ dW = 84 + 84 × 20 = 84 × 21
⇒ dW = 1764 J
(c) Using the first law of thermodynamics, we get
Work is done by the system. Thus, work done is negative.
⇒ dQ = 0 (given)
dU = − dW
= (1764) = 1764 J