A perfectly insulated tank of negligible heat capacity contains P lb of brine at T, = 30°F. Hot brine at 100°F runs into the tank at the rate of 3 lb/min, and the brine in the tank, brought instantly to uniform, temperature throughout by vigorous stirring, runs out at the same rate. If the specific heat of the brine is c, =1 btu/lb-°F, find the temperature of the brine in the tank as a function of time. Use ho=1200 btu/lb, initial mass inside the tank P = 50 lb, and the amount of heat in the brine at a particular temperature is H = P[c»(T – T,) + ho]. The change in the heat content in the brine during the time interval dt is dH. -

A perfectly insulated tank of negligible heat capacity contains P lb of brine at T, = 30°F. Hot brine at 100°F runs into the tank at the rate of 3 lb/min, and the brine in the tank, brought instantly to uniform, temperature throughout by vigorous stirring, runs out at the same rate. If the specific heat of the brine is c, =1 btu/lb-°F, find the temperature of the brine in the tank as a function of time. Use ho=1200 btu/lb, initial mass inside the tank P = 50 lb, and the amount of heat in the brine at a particular temperature is H = P[c»(T – T,) + ho]. The change in the heat content in the brine during the time interval dt is dH. -