A cup of water at 5°C (system) is placed in a microwave oven and the oven is turned on for one minute during which the water begins to boil. Which of the following option is true ?
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In thermodynamics, always remember the IUPAC convention: energy into the system is positive ($q>0$), and work done by the system is negative ($w<0$).
To analyze the changes in the system when a cup of water at 5°C is placed in a microwave oven and heated until it begins to boil, we need to consider the basic principles of thermodynamics involving heat transfer (q), work done (w), and internal energy change (ΔU).
Understanding the system and process: When the microwave oven is turned on, the water absorbs heat energy to increase its temperature until it reaches the boiling point. In thermodynamic terms:
\(q\) (heat absorbed) is positive, as heat is added to the system.
\(w\) (work done by the system) is negative or zero in this context. There is no volume change since the water is simply heating up, not expanding in doing work like pushing a piston.
\(\Delta U\) (change in internal energy) is positive, as the temperature increase raises the internal energy.
Evaluating the options:
\(q = +ve\), \(w = 0\), \(\Delta U = -ve\) - Incorrect because ΔU is positive with the temperature increase.
\(q = +ve\), \(w = -ve\), \(\Delta U = +ve\) - Correct, as all these conditions match our analysis: heat is absorbed, the system does no work, and internal energy increases.
\(q = +ve\), \(w = -ve\), \(\Delta U = -ve\) - Incorrect because ΔU cannot be negative in the process described.
\(q = -ve\), \(w = -ve\), \(\Delta U = -ve\) - Incorrect as this would imply cooling, which does not occur.
Conclusion: The correct thermodynamic description of the process where water is heated in the microwave and begins to boil is that \(q = +ve\), \(w = -ve\), and \(\Delta U = +ve\).
This can be explained by the first law of thermodynamics: \(\Delta U = q + w\). Heat is absorbed by the water, causing a rise in temperature which increases the internal energy, and no significant work is done by the system in this process.
