Question

For the question (7) below please do the following:

Draw a picture of the system. Name an extensive property that can be counted. Label the system, surroundings, and system boundary. State the time period of interest. Justify. Identify the system as open, closed, or isolated and state why. Identify the system as steady-state or dynamic and state why. Identify whether the system has a reaction and/or energy interconversion and state why. Should an algebraic, differential, or integral equation be used to describe the system? State why. Is the selected extensive property conserved in this system? State why.

Q7. Soon after you wake up on a mid-December morning, you grab a cup of hot coffee. You instantly feel the warmth of the mug in your hand. You would like to know how the rate of energy flow from the cup to your hand changes with time.

Answer 1

The system is formed by the Hot cofee, the Cofee Mug and the Hand. The extensive property that can be counted is the temperature of the cofee. We could enclose the system in a control volume, limited by a control surface, which acts as a boundary separating from the sorrounding atmosphere (the surroundings is the air at room temperature). The time period of interest is the amount it takes the cofee to get to room temperature. The system is closed because no mass is flowing in or out through the boundary, but there is a net exchange of energy with the surroundings. It's a dynamic state system, because the heat flow rate changes with time (it decreases as times goes by). There's no reaction (no heat generation inside the control volume) and no energy interconversion, only thermal energy flowing through various resistances (convective and conductive). A differential equation should be used to describe this system, because the properties are changing and the energetic balance must be met at all times. To simplify our model we could consider the Temperature independent of the position inside each phase of the control volume (coffee-mug-hand), but it will vary with time.