An engineer is developing an electric water heater to provide a continuous supply of hot water. One trial design is shown in Fig. Water is flowing at the rate of 0.500 kg/min, the inlet thermometer registers 18.0°C, the voltmeter reads 120 V, and the ammeter reads 15.0 A [corresponding to a power input of (120 V) × (15.0 A) = 1800 W]. (a) When a steady state is finally reached, what is the reading of the outlet thermometer? (b) Why is it unnecessary to take into account the heat capacity ?mc? of the apparatus itself? Figure:

Solution 119P Step 1: The equation for specific heat, Q = mCT Where, m - mass of the object C - Specific heat capacity of the substance T - Change in temperature of the system Step 2: The heat energy input is through the electrical energy. Electric power, P= VI = 1800 W Total energy, Q = Pt So, we can write, VIt = mCT Or, VI = (m/t) CT Here, we are using water. So, the specific heat capacity of water, C water 4184 J/ kg K m/t is nothing but the rate of mass flow. Provided, m/t = 0.500 kg/min We know that, 1 min = 60 seconds Therefore, m/t = 0.500/60 kg/s = 0.008 kg/s