8. A bicycle pump contains 70 cm3 of air at a pressure of 1.0 atmosphere and a temperature of 7°C. Whenthe air is compressed to 30 cm3 the temperature rises to 27 °C.This is because the person is doing work on the gas inside thepump, which increases the internal energy of the gas. Themolecules move faster and the temperature rises. What is thepressure now?Ans:
Question
- A bicycle pump contains 70 cm3 of air at a pressure of 1.0 atmosphere and a temperature of 7°C. Whenthe air is compressed to 30 cm3 the temperature rises to 27 °C.This is because the person is doing work on the gas inside thepump, which increases the internal energy of the gas. Themolecules move faster and the temperature rises. What is thepressure now?Ans:
Solution
To solve this problem, we can use the ideal gas law, which states that the product of the volume and pressure of a gas is directly proportional to the temperature. This can be written as:
P1V1/T1 = P2V2/T2
Where: P1 = initial pressure = 1.0 atm V1 = initial volume = 70 cm3 T1 = initial temperature = 7°C = 280.15 K (converting from Celsius to Kelvin by adding 273.15)
P2 = final pressure (what we're trying to find) V2 = final volume = 30 cm3 T2 = final temperature = 27°C = 300.15 K (converting from Celsius to Kelvin by adding 273.15)
Rearranging the equation to solve for P2 gives us:
P2 = P1V1T2 / T1V2
Substituting the known values into the equation gives us:
P2 = (1.0 atm * 70 cm3 * 300.15 K) / (280.15 K * 30 cm3)
Solving this equation gives us the final pressure, P2.
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