Ch 3 P40 A gas is contained in a closed rigid tank. An electric resistor in the
ID: 1848134 • Letter: C
Question
Ch 3 P40
A gas is contained in a closed rigid tank. An electric resistor in the tank transfers energy to the gas at a constant rate of 1000W. Heat transfer between the gas and the surroundings occurs at a rate of Q=-50t, where Q is in watts, and t is time, in min.
a. Plot the time rate of change of energy of the gas for 0 to 20 min, in watts.
b. Determine the net change in energy of the gas after 20 min, in kJ.
c.If electricity is valued at $0.08 per kW*h, what is the cost of the electrical input to the resistor for 20 min of operation?
Explanation / Answer
Q(t) = 1000 watt - 50 (watt / min ) t For example, when t = 5 min, the energy that is absorbed inside the tank is: Q(5 min) = 1000 watt - 50 (watt / min) 5 min = 750 watt The total energy absorbed is: Energy = power X time or E = P t or dE = P dt and E = Integral (Q (t) ) dt