An engineer is developing an electric water heater to provide a continuous (\"on

Question

An engineer is developing an electric water heater to provide a continuous ("on demand") supply of hot water. One trial design is shown in the figure. (Figure 1) Water is flowing at the rate F, the inlet thermometer registers T1, the voltmeter reads V, and the ammeter reads current I. Then the power (i.e., the heat generated per unit time by the heating element) is VI.

Assume that the heat capacity of water is C and that the heat capacity of the heater apparatus is Ch.

Part A

When a steady state is finally reached, what is the temperature reading T2 of the outlet thermometer?

Express the outlet temperature in terms of T1, F, C, and any other given quantities.

Explanation / Answer

the energy with change in temperature is

E = m X C X dT

v X i X t = m X C X dT

but change in in temperare is

dT = ( Tf - Ti )

v X i X t = m X C X ( Tf - Ti )

v X i = ( m / t ) X C X ( Tf - Ti )

v X i = F X C X ( Tf - Ti )

Tf = ( ( v X i ) / ( F X C ) ) + Ti

the temperature reading T2 of the outlet thermometer is Tf = ( ( v X i ) / ( F X C ) ) + Ti

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