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Question: A \(2100W\) continuous flow geyser (instant geyser) has water inlet temperature \({{10}^{0}}C\)while...

A 2100W2100W continuous flow geyser (instant geyser) has water inlet temperature 100C{{10}^{0}}Cwhile the water flows out at the rate of 20gs−120g{{s}^{-1}}. The outlet temperature of water must be about
a)20 b)30 c)35 d)40 \begin{aligned} & a)20 \\\ & b)30 \\\ & c)35 \\\ & d)40 \\\ \end{aligned}

Explanation

Solution

Let us first find the mass of water flowing out in terms of kilograms. As power is equal to the product of mass, temperature difference and the heat capacity. As we know the heat capacity of the water, the mass of the water flowing out of the geyser and temperature initially, we can easily find the outlet temperature.
Formula used:
P=mcΔTP=mc\Delta T

Complete answer:
Given the mass of water exiting the valve, lets us convert it into kilogram per second,
m=20gs−1=20×10−3m=20g{{s}^{-1}}=20\times {{10}^{-3}}
Now, the heat capacity of the water is given as 42004200,
Let’s substitute these values above, we get,
P=mcΔT ⇒P=20×10−3×4200×(T−10) ⇒2100=20×10−3×4200×(T−10) ⇒T=350C \begin{aligned} & P=mc\Delta T \\\ & \Rightarrow P=20\times {{10}^{-3}}\times 4200\times (T-10) \\\ & \Rightarrow 2100=20\times {{10}^{-3}}\times 4200\times (T-10) \\\ & \Rightarrow T={{35}^{0}}C \\\ \end{aligned}

So, the correct answer is “Option C”.

Additional Information:
Power is the unit of energy per unit of time. Power units are watts. One joule is equal to one watt during one second. One joule is one newton meter. One watt per hour is equal to three thousand six hundred joules. Thermal energy is the energy generated from heat. This heat is produced by the movement of small particles within an object. The faster the particles move; the more heat is generated. Thermal energy is responsible for the temperature of the system and a part of total energy of the system. It is usually expressed in q. The power in thermodynamics can be equal to the thermal energy formula which depends on the mass, specific heat and the temperature difference.

Note:
In thermal sources, there are two major areas of concern. The first area is the temperature bias or offset from ideal temperature. The next problem arises when there is a presence of time varying thermal disturbance with respect to the machine to a periodic function.