5a. A Stirling engine is a unique heat engine invented by Robert Stirling in 1816. Unlike a Brayton cycle gas turbine or an internal combustion engine, a Stirling engine uses an external heat source that heats a trapped internal gas. You may remember another device that uses an external heat source is a drinking bird. Stirling engine systems are sometimes used in thermal concentrating solar power systems. Consider a Stirling engine power system for household use that is guaranteed to last 15 years and is fueled by burning natural gas with a combined combustion and heat transfer efficiency of 89.0%, a cycle efficiency of 41.0 %, and a generation efficiency of 95.0%. Operations and maintenance costs total $0.01/kWh. Assume natural gas costs will be $7.00/MBtu for the next 15 years and an interest rate of 6% and financing for 15 years. Assume a house requires 20 kWh per day and you currently pay $0.175/kWh and you anticipate this will remain constant for the next 15 years. Assume that this system will be a grid-tied system buy power from and sell power to the grid at the same price. What is the overall efficiency of the Stirling engine system (%)? What is the cost of fuel per kWh ($/kWh)? If you are willing to spend no more than 80% of your current electrical costs on this system, what is the maximum you should pay for the Stirling engine system ($)?