Question

7.4) A 860 MW power plant uses steam at 600 K as its input heat and deposits its waste heat into a river at 285 K. Model the power plant as an ideal Carnot heat engine.

a. If the water flow rate of the river is 36.7 m3/s, find the temperature increase down river from the power plant.

**First figure out the efficiency of the power plant. Next figure out how much heat per unit time the power plant is depositing in the river. To figure out how much this warms the river water, use Q = m c ΔT, divided by time t. So the left-hand-side is Q/t, the rate at which the water is heated, and the right-hand-side contains m/t the mass rate of flow of water. Using the density of water and the given volume rate of flow, you can figure out the mass rate of flow.

b. Calculate the amount by which the entropy of a kilogram of river water is increased, in units of J/kg.K. The initial temperature of the river is 12 degrees Celsius.

Answer 1

It is given in the Question that given system is an Ideal Carnot Heat Engine. Hence, its efficiency is given by:

Where,

We get,

(a)   0.57 or 57%. Now the amount of heat generated is to be computed.

(i) First, we need to compute the mass of water flowing:

Using the density of water we calculate the mass of water flowing per second.

(ii) Now, heat transferred per second or simply power can be computed using a simple formula:

Here,

That comes out to be =

But as it can be noticed this water might be used to do some work because it is given that powerplant has an output of 860 MW. So, we need to subtract the Energy from the one we get from the above formulation. It comes out to be

Which you see has very less change Hence, our final answer for part (a) is  

Here there is no worry for (internal energy) as the process is given ideal.

(b) Now to compute the entropy change for this Carnot cycle with given information is computed using:

Here,

Substituting the values in the above formula we get:

Note: Though I took care of calculations it is advised to perform a recheck for calculations.