Question

Consider a classroom filled with air. Let’s approximate air as an ideal gas of N2-molecules (nitrogen) at normal conditions (P = 1 Bar and T = 300 Kelvin). Suppose the room has dimensions of 10 m by 10 m by 10 m (a pretty large auditorium). Let us also assume that N2 molecule has 5 degrees of freedom (3 translational and 2 rotational). In this problem you will need to provide numeric answers up to the first significant digit.

2.1 [2pt] How much gas [in moles] is there in the room?
2.2 [1pt] How may molecules of gas are there in the room?

2.3 [2pt] What is the mean distance between gas molecules?

2.4 [1pt] If all the gas condenses into a liquid collected into a jar, how much would it weight?

2.5 [1pt] What is the r.m.s. velocity of the gas molecules in m/s?

2.6 [2pt] What is the ratio of the r.m.s. velocity of the gas molecules to the speed of sound in the room?

2.7 [2pt] Is it likely to find a molecule which moves at the speed of 1 miles/hour? 1000 miles/hour? 1 000 000 miles/hour?

2.8 [2pt] What is the force the gas exerts at the floor of the room? How does it compare to the total force a class of 50 students weighting 100 pounds each exerts at the floor?

2.9 [2pt] Let’s assume your ear drum has an area of 1 cm^2. How many gas molecules hit your eardrum every second? An order of magnitude answer would suffice.

2.10 [1pt] What is the total internal energy of the gas in calories?

2.11 [2pt] Nitrogen condenses into a liquid at a temperature of about 77K. How much heat do we need to extract from the gas for it to begin to condense? Assume the process is constant volume. Express it in calories.

2.12 [2pt] In Q2.11, how much extra heat is needed to condense all the gas to a liquid? Express it in calories.

2.13 [2pt] When metals cool down they contract and this contraction usually stops at liquid nitrogen temperatures. Suppose we have inserted a copper cylinder inside a piece of brass. The fit is tight at room temperature. Brass contracts more than copper upon cooling down. Estimate the pressure on the brass. Express it in units of N/m^2 and compare it to the pressure a human being exerts on the ground.

Answer 1