Problem 3 (20 points) - Energy balance
One kilogram of Refrigerant, initially at $P_1 = 0.9$ MPa, $u_1 =232.92$ kJ/kg, is contained within a rigid closed
tank. The tank has a resistive heater inside with a voltage of 120 V and current of 2 A. The instantaneous
rate of heat transfer between the surroundings and the refrigerant is $\dot{Q}(t) = Kt$, where K is a positive
constant with units of kW/minute, and t is the time in minutes. After 20 minutes of heating, the
refrigerant properties change to $P_2 = 1.2$ MPa, $u_2 =276.67$ kJ/kg. There is no change in the kinetic or
potential energy in the tank (i.e., this is a stationary system). Please answer the following.
i. For the refrigerant, determine the electrical work and heat transfer during the 20-minute duration
of the process, in kJ. Be sure to include a schematic of your system and to indicate the direction
of the relevant energy transfers (i.e., either into the system or out of the system). List your
assumptions as you perform your analysis.
ii. Determine the value of the constant K appearing in the given heat transfer equation, in kW/min.
(Hint: how do you relate the instantaneous heat transfer rate, $\dot{Q}(t)$, to the total heat transfer, Q,
over some time interval?)
