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 ?

• Heat ($$q$$): The system absorbs radiation energy from the microwave, increasing its thermal energy. Since energy enters the system, heat is positive ($$q = \text{+ ve}$$).
• Work ($$w$$): As the water heats up and begins to boil, it turns into vapor and expands against atmospheric pressure. Since work is done by the system on the surroundings, work is negative ($$w = \text{- ve}$$).
• Internal Energy Change ($$\Delta U$$): The temperature of the water rises significantly from $$5^\circ\text{C}$$ to its boiling point ($$100^\circ\text{C}$$). Since internal energy is a direct function of temperature ($$U \propto T$$), it increases ($$\Delta U = \text{+ ve}$$).

Conclusion:

The process involves absorption of energy resulting in expansion work and a net rise in temperature, making $$q = \text{+ ve}$$, $$w = \text{- ve}$$, and $$\Delta U = \text{+ ve}$$.

Answer: Option C — $$q = \text{+ ve}, w = \text{- ve}, \Delta U = \text{+ ve}$$