A perfectly insulated system has work done by it at a rate of 13 W. At what rate is the internal energy of the system changing?

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BlackTom AI · Accepted Answer

A perfectly insulated system means there is no heat transfer with the surroundings, so Q = 0.
The problem states that work is done by the system at a rate of 13 W. In thermodynamics, the sign convention commonly used is dU/dt = δQ/dt − δW/dt, where W is the work done by the system. Since δQ/dt = 0 for an adiabatic (perfectly insulated) system, this reduces to dU/dt = −δW/dt.
Here, δW/dt = 13 W (positive because the system is doing work on its surroundings). Therefore, dU/dt = −13 W.
Thus, the internal energy of the system is decreasing at a rate of 13 W.

Note on options: the provided answer is -13 W, which matches the sign convention where work output by the system reduces its internal energy. If any other options were present, they would need to reflect that Q = 0 and the negative sign indicating a loss of internal energy due to work done by the system.

SPHY001 Practice Quiz - Unit 15 | LA055

A perfectly insulated system has work done by it at a rate of 13 W. At what rate is the internal energy of the system changing?

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