Final answer:
The initial pressure of the bicycle tire is 7.00×10µ N/m², and after letting out 100 cm³ of air, the pressure should mathematically decrease. However, the correct final pressure is not among the provided options because the adjustment for atmospheric pressure was not considered in the options.
Step-by-step explanation:
To determine the new pressure in the bicycle tire after letting out 100 cm³ of air at atmospheric pressure, we can use the ideal gas law, which states that for a given amount of gas, the product of pressure and volume is constant if the temperature and the amount of gas remain unchanged. Given that the initial pressure is 7.00×10µ N/m², and the initial volume is 2.00 L (which is 2000 cm³), we can calculate the final pressure after letting out 100 cm³ of air.
The final volume of the gas will be 2000 cm³ - 100 cm³ = 1900 cm³. Using the formula (P1V1 = P2V2), where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume, we get:
7.00×10µ N/m² × 2000 cm³ = P2 × 1900 cm³
P2 = (7.00×10µ N/m² × 2000 cm³) / 1900 cm³
P2 = 7.37×10µ N/m²
However, since we're releasing the air at atmospheric pressure, we must subtract the atmospheric pressure from the final pressure calculated. Assuming that atmospheric pressure is approximately 1.013×10µ N/m², the adjusted final pressure in the tire would be:
P2 = 7.37×10µ N/m² - 1.013×10µ N/m²
P2 = 6.36×10µ N/m²
Looking at the options provided, none of them accurately reflect the calculated result due to the oversight of subtracting atmospheric pressure. If we assumed no adjustment for atmospheric pressure, the closest answer to our calculation would be 6.86×10µ N/m² (option a), but this fails to consider the released air at atmospheric pressure. Therefore, the options provided do not offer the correct answer.