Homework 2

Problem 1

Draw PV and TS diagrams for the Carnot refridgeration 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

$$Δ\dot{S} = \dot{S}{in} - \dot{S}{out} + \dot{S}_{gen}.$$

Is $\dot{S}_{gen}$ greater than, less than, or equal to zero for a real process? What about an irreversible process? Consider the following image:

Assuming each system is at steady state, 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 a compression ratio of 12 and for high and low temperatures of 1800 K and 300 K.

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 (CH4 + 2O2+ 7.52N2 = CO2 + 2H2O + 7.52N2), with 300 K and 1 atm ambient conditions. Use a compression ratio of 12.

Problem 6

Derive the expression for the Diesel efficiency.

Problem 7

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.