The CBE 100 final exam is early in the morning (or late into the night) and...

  

Transcribed Image Text:

The CBE 100 final exam is early in the morning (or late into the night) and so you decide a little coffee will help. You pour leftover coffee at 15C inside a Styrofoam cup and place it in the microwave. Treat the coffee as having properties of water that can be treated as constants; for example, specific heat can be treated as a constant here. The microwave will transfer 950W of power into the liquid coffee (no heat going into the air or the cup). The Styrofoam cup you use holds 485 mL of liquid. You like your coffee hot at a temperature of 75C. a) (7 pt) Assuming that the coffee is well-insulated (all power of microwave is transferred to the liquid coffee, and no heat is lost to the air in the microwave) and neglecting evaporation, how long should you run the microwave oven to heat the coffee initially at 15C to 75C? (to the nearest second). Hint: do differential energy balance on this system (closed or open?). b) (8 pt) In reality, the Styrofoam does not provide perfect insulation. This means that while heat is transferred from the microwave to the liquid coffee at a rate of Qmicrowave = 950W, heat is also leaving the coffee at the same time through convection at a rate given by: Qconvection = h * (Tcoffee - Tair) Where h = 0.5 W/C, Tcoffee is the temperature of the coffee, and Tair is constant at 15 C. Still neglecting evaporation but now considering that heat can be lost through convection, how long should you run the microwave? Based on this answer, was the assumption of well- insulated you made in part (a) a good assumption? The CBE 100 final exam is early in the morning (or late into the night) and so you decide a little coffee will help. You pour leftover coffee at 15C inside a Styrofoam cup and place it in the microwave. Treat the coffee as having properties of water that can be treated as constants; for example, specific heat can be treated as a constant here. The microwave will transfer 950W of power into the liquid coffee (no heat going into the air or the cup). The Styrofoam cup you use holds 485 mL of liquid. You like your coffee hot at a temperature of 75C. a) (7 pt) Assuming that the coffee is well-insulated (all power of microwave is transferred to the liquid coffee, and no heat is lost to the air in the microwave) and neglecting evaporation, how long should you run the microwave oven to heat the coffee initially at 15C to 75C? (to the nearest second). Hint: do differential energy balance on this system (closed or open?). b) (8 pt) In reality, the Styrofoam does not provide perfect insulation. This means that while heat is transferred from the microwave to the liquid coffee at a rate of Qmicrowave = 950W, heat is also leaving the coffee at the same time through convection at a rate given by: Qconvection = h * (Tcoffee - Tair) Where h = 0.5 W/C, Tcoffee is the temperature of the coffee, and Tair is constant at 15 C. Still neglecting evaporation but now considering that heat can be lost through convection, how long should you run the microwave? Based on this answer, was the assumption of well- insulated you made in part (a) a good assumption?