Op-amps often serve as building blocks in analog control systems. The objective of this example is to illustrate the use of op-amps in a temperature control circuit. Figure 6.33(a) depicts a system for which the temperature is to be maintained constant at 20C in a variable temperature environment. The system temperature is measured via a thermocouple (see the Temperature Measurement section in Chapter 7). Heat is added to the system by a coil of resistance R_coil. The heat flux is q_in = i 2Rcoil, where i is the current provided by a power amplifier. The system is insulated on three sides. The fourth side is not insulated such that heat is transferred across the boundary by convection, which is represented by an equivalent thermal resistance R_t. The system has mass m, specific heat c, and thermal capacitance C_t = mc (see the Make the Connection boxes Thermal Capacitance and Thermal System Dynamics in Chapter 4).