Determine whether the sign of heat or work (relative to the system) is positive or negative. a metal cylinder is rolled up a ramp. (the metal cylinder is the system.) the fireman extinguishes the fire with foam and cools the environment. (the foam is the system.)

Metal cylinder: Work is positive

Foam: Heat is positive.

Explanation:

Work is done as a resultant force acts along a displacement. Heat is the flow of energy from one body to another, resulting in a either a rise or a drop in temperature of the bodies. Work and Heat are forms of energy and they can either be assigned a positive or negative sign with respect to a thermodynamic system.

If work is done on a body (thermodynamic system), the work is negative. On the other hand, if work is done by the body, it is termed as a positive work. Heat is positive when it flows into a thermodynamic system and negative when it is lost by the system.

In this case, though the metal cylinder is rolled up a ramp, the metal cylinder does a positive work along the displacement. Considering the foam, heat is gained by the foam (thermodynamic system) as it cools the environment, thus, heat is positive.