Question

The mean free path of a molecule in a gas is 300nm .

Part A
What is the mean free path if the gas temperature is doubled at constant volume?
Express your answer to two significant figures and include the appropriate units.
Part B
What is the mean free path if the gas temperature is doubled at constant pressure?
Express your answer to two significant figures and include the appropriate units.

Answer 1

To calculate the minimum stopping distance, consider the force of static friction on different road conditions. For a rainy day and dry surface, use the given coefficients of static friction to calculate the distance over which the force can decelerate the car to a stop.

Step-by-step explanation:

To calculate the minimum stopping distance, we need to consider the force of static friction. The force of static friction can be calculated by multiplying the coefficient of static friction by the normal force. On a horizontal surface, the normal force is equal to the weight of the car, which can be calculated by multiplying the mass of the car by the acceleration due to gravity.

(a) On a rainy day, the coefficient of static friction is given as 0.105. So, the force of static friction is 0.105 times the weight of the car. To find the minimum stopping distance, we need to calculate the distance over which this force can decelerate the car to a stop.

(b) When the surface is dry, the coefficient of static friction is given as 0.597. Following the same process as in part (a), we can calculate the minimum stopping distance.

Answer 2

Part A - Final Answer:

If the gas temperature is doubled at constant volume, the mean free path of a molecule becomes approximately 424 nm.

Part A - Explanation:

The mean free path of gas molecules is inversely proportional to temperature. According to the kinetic theory of gases, the mean free path (λ) is given by the formula
`\(λ = (kT)/(√(2)\pi d^2P)\)`, where (k) is the Boltzmann constant, (T) is the temperature, \d) is the diameter of the gas molecules, and (P) is the pressure. If the gas temperature is doubled at constant volume, the temperature (T) in the formula becomes 2(T). Considering the temperature doubling, the mean free path is calculated using the formula.

Part B - Final Answer:

If the gas temperature is doubled at constant pressure, the mean free path of a molecule becomes approximately 300 nm.

Part B - Explanation:

At constant pressure, the mean free path is given by the formula
`\(λ = (kT)/(√(2)\pi d^2P)\).` Similar to Part A, if the gas temperature is doubled, the temperature (T) in the formula becomes 2(T). Plugging in this value into the formula, we can calculate the new mean free path. It's important to note that constant pressure conditions affect the relationship between temperature and mean free path differently than constant volume conditions, leading to different results in Parts A and B.