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The temperature of an open room of volume 30 m³ increases from 17°C to 27°C due to sunshine. The atmospheric pressure in the room remains 1 × 10⁵ Pa. If n_i and n_f are the number of molecules in the room before and after heating, then n_f − n_i will be:

1. 2.5 × 10²⁵
2. −2.5 × 10²⁵
3. −1.61 × 10²³
4. 1.38 × 10²³

Correct answer: −2.5 × 10²⁵

Solution

As the temperature increases, the volume of gas remains constant, leading to an increase in pressure. However, since the room is open to the atmosphere, the gas can escape, resulting in a decrease in the number of molecules, hence n_f - n_i is negative.

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