Question

Thermodynamics deals with the macroscopic properties of materials. Scientists can make quantitative predictions about these macroscopic properties by thinking on a microscopic scale. Kinetic theory and statistical mechanics provide a way to relate molecular models to thermodynamics. Predicting the heat capacities of gases at a constant volume from the number of degrees of freedom of a gas molecule is one example of the predictive power of molecular models.

The molar specific heat Cv of a gas at a constant volume is the quantity of energy required to raise the temperature T of one mole of gas by one degree while the volume remains the same. Mathematically,

Cv=1nΔEthΔT,

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. Some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. No water tank is involved, so no heat is wasted. A typical household shower flow rate is 2.51 gal/min (9.49 L/min) with the tap water being heated from 49.0 ∘F (9.44 ∘C) to 122 ∘F∘F (50.0 ∘C) by the on-demand heater.

What rate of heat input (either electrical or from gas) is required to operate such a unit, assuming that all the heat goes into the water?

Answer 1

The concept used in this question is energy conservation principle ,as it is also mention in the question that all the heat goes in to the water means no heat is wasted . I just apply this concept and finally deduced the values.

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