Homework 2

Problem 1

Draw PV and TS diagrams for the Carnot refrigeration cycle. Outline the steps. What is the thermodynamic efficiency for an average Provo high temperature in July?

Problem 2

An entropy balance is given by $$\Delta\dot{S} = \dot{S}{in} - \dot{S}{out} + \dot{S}{gen}$$. Is $\dot{S}{gen}$ greater than, less than, or equal to zero for a real process? Consider the following image:

Determine if each system is feasible. If it is, find an example for the system (e.g., heat engine, electric heater, etc.).

Problem 3

What is the difference between a refrigerator and a heat pump?

Compare the power requirements of an electric heater and a Carnot heat pump used to heat a house to 20 $^oC$ with an outside temperature of 0 $^oC$.

Problem 4

Compute thermal efficiencies of the ideal Carnot, Otto, Diesel, and Brayton cycles for high and low temperatures of 1800 K and 300 K. Use a a compression ratio of 12 for Otto and Diesel, and a pressure ratio of 12 for Brayton.

Problem 5

Compare the Otto engine efficiency computed using the simple air standard assumptions with a more complex equilibrium calculation using the online combustion tool assuming a stoichiometric methane-air mixture with 300 K and 1 atm ambient conditions. Use a compression ratio of 12.

Problem 6

Compute the work potential of 1 lbm/s of superheated steam at 500 $^oF$ and 200 psia when transformed to liquid water at 77 $^oF$ and 14.696 psia. Here’s a link to the online vapor/liquid properties tool