Chapter 3, Problem 27PP

Crop damage due to frost is one of the many risks confronting farmers. The figure below shows a simple alarm circuit designed to warn of frost. The alarm circuit uses a device called a thermistor to sound a buzzer when the temperature drops below freezing. Thermistors are semiconductor devices that exhibit a temperature dependent resistance described by the equation

$R=R_0{e}^{{}_{{}^{\beta \left(\frac{1}{T}-\frac{1}{T_0}\right)}}}$

where R is the resistance, in Ω, at the temperature T, in °K, and R₀ is the resistance, in Ω, at the temperature T₀, in °K. β is a constant that depends on the material used to make the thermistor.

The circuit is designed so that the alarm will sound when

$\frac{R_2}{R+R_2}<\frac{R_4}{R_3+R_4}$

The thermistor used in the alarm circuit has R₀ = 33,192 Ω at T₀ = 40 °c, and β = 3,310 °K. (Notice that β has units of °K. The temperature in °K is obtained by adding 273° to the temperature in °C.) The resistors R₂, R₃, and R₄ have a resistance of 156.3 kΩ = 156,300 Ω.

Write a Java program that prompts the user for a temperature in °F and prints a message indicating whether or not the alarm will sound at that temperature.