A perfectly insulated system has work done by it at a rate of 20 W. At what rate is the internal energy of the system changing?

Question

BlackTom AI · Accepted Answer

Start by identifying the key physics principle involved: the first law of thermodynamics, which relates the change in internal energy to heat transfer and work done. For any system, ΔU = Q − W, where W is the work done by the system on its surroundings and Q is the heat added to the system.

For a perfectly insulated (adiabatic) system, there is no heat exchange with the surroundings, so Q = 0.

The problem states that work is done by the system at a rate of 20 W. Since W represents work done by the system, W = +20 W in the ΔU = Q − W convention.

Plugging in the values: ΔU = 0 − 20 W = −20 W. This means the internal energy of the system is decreasing at 20 W.

Now evaluate each option:

- Option: 40 W. This would imply a positive increase in internal energy, which contradicts the no-heat-transfer condition and the presence of work done by the system; therefore this is incorrect.

- Option: 0 W. A zero rate of change would require no work or heat exchange. Since the system does work and heat transfer is zero, this cannot be correct.

- Option: −20 W. This matches the calculation from the first law with Q = 0 and W = 20 W, yielding a decrease in internal energy at 20 W. This is the correct description of the rate of change.

- Option: 20 W. A positive 20 W would imply the internal energy is increasing, which would require either heat input or work done on the system, neither of which aligns with the given conditions (work done by the system and no heat exchange). Therefore this is incorrect.

SPHY001 Graded Quiz 8 (Unit 15 and Unit 16)- Requires Respondus LockDown Browser

A perfectly insulated system has work done by it at a rate of 20 W. At what rate is the internal energy of the system changing?

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