A cup of water at 5°C is placed in a microwave oven and begins to boil
Q. 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?
A. \( q = +ve,\; w = -ve,\; \Delta U = +ve \)
B. \( q = +ve,\; w = 0,\; \Delta U = -ve \)
C. \( q = +ve,\; w = -ve,\; \Delta U = -ve \)
D. \( q = -ve,\; w = -ve,\; \Delta U = -ve \)
Correct Answer: A

Explanation

The system is water kept inside a microwave oven. When the oven is switched on, energy is supplied to the system, hence heat absorbed by the system is positive.

Therefore,

$$ q = +ve $$

As the water starts boiling, it expands against atmospheric pressure and does work on the surroundings. Hence, work done by the system is negative.

$$ w = -ve $$

According to the first law of thermodynamics,

$$ \Delta U = q + w $$

Since the magnitude of heat supplied is greater than the work done during heating and boiling, the internal energy of the system increases.

$$ \Delta U = +ve $$

Thus, the correct option is:

$$ \boxed{q = +ve,\; w = -ve,\; \Delta U = +ve} $$

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