A system has a heat source supplying heat at a rate of 187 W and is doing work at a rate of 130 W. At what rate is the internal energy of the system changing?

Question

BlackTom AI · Accepted Answer

To determine how fast the internal energy is changing, we apply the first law of thermodynamics in rate form:

ΔU̇ = Q̇ − Ẇ

Where:
- Q̇ is the heat added to the system (positive if heat flows into the system). Here, the heat source supplies heat at a rate of 187 W, so Q̇ = +187 W.
- Ẇ is the work rate done by the system (positive if the system does work on the surroundings). The problem states the system is doing work at a rate of 130 W, so Ẇ = +130 W.

Plugging in these values:
ΔU̇ = 187 W − 130 W = 57 W

This means the internal energy of the system is increasing at a rate of 57 watts (i.e., 57 joules per second). Note on sign conventions: if you use the opposite sign convention for work (work done on the system as negative), you would get ΔU̇ = Q̇ + Ẇ′ with Ẇ′ = −130 W, which still yields 187 − (−130) = 317 W, so it is crucial to consistently use the chosen convention. In this problem, the standard thermodynamic convention (work done by the system positive) gives ΔU̇ = +57 W.

Since the problem provides Q̇ and Ẇ directly, no other data are needed to compute the rate of change of internal energy. If an option list existed, you would compare the computed value to the given choices to identify the match.

A system has a heat source supplying heat at a rate of 187 W and is doing work at a rate of 130 W. At what rate is the internal energy of the system changing? Single choice

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