Question

Asked Oct 9, 2019

A 3 Kg mass of water is heated to a temperature of 99.5 C at 1 bar of pressure. It is slowly poured into a heavily insulated beaker containing 7.5 Kg of water at a temperature and pressure of 4 C, 1 bar, respectively. The specific heat of the water, an incompressible material is, c = 4.1 KJ/(Kg K). The beakers are an adiabatic system. The two water mass’ reach an equilibrium temperature. There is no kinetic or potential energy change in this problem.

- Using the first law determine the final temperature of the water in the beaker.
- Calculate the entropy production in this process. (Hint: note that this is an incompressible material which means that the density and specific volume are constant)

Step 1

The mass of water m_{1} = 3kg

The water is heated to a temperature of T_{1} = 99.5^{o}C

The mass of water in the insulated beaker m_{2} = 7.5 kg

The temperature of the water inside the beaker T_{2} = 4^{o}C

The pressure inside the insulated beaker P_{2} = 1 bar

The specific heat of water c_{p} = 4.1 KJ/kgK

Step 2

The final temperature of water can be calculated with the help of First law of thermodynamics. The first law of thermodynamics is the law of conversation of energy for the thermodynamic systems. According to the conservation of energy, the energy given by one system is received by another system if there is no loss to the surrounding.

The energy balance equation gives

Step 3

Part (b)

The entropy production in the process:

First calculate the entrop...

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