Gas Laws

To solve this problem, we apply the Ideal Gas Law, given by the equation , where is pressure, is volume, is the amount of substance in moles, is the gas constant, and is the temperature in Kelvin. Initially, the two bulbs (400 cm and 200 cm ) are at 20°C, and 1.000 atm. Converting temperatures to Kelvin, we have:

When the larger bulb is placed in steam, its temperature becomes:

The smaller bulb in ice has a temperature:

Initially, the total volume is 600 cm with air at 293.15 K and 1.000 atm pressure. Using the Ideal Gas Law for the whole system:

, where , , and remain constant for the system.

After the temperature change when the larger bulb is at 373.15 K and the smaller at 273.15 K, and the pressure equilibrates to , the equation for the larger bulb is:

And the equation for the smaller bulb is:

Since air is distributed according to temperatures, is conserved:

Using the Ideal Gas Law for both bulbs and combining terms, we get:

Combining,

Simplifying gives:

Solving for ,

Thus, the final common pressure is 1.13 atm.

The speed of gas molecules is related to the temperature and molecular weight by the formula: where is the speed, is the temperature, and is the molecular weight. Since the speeds of hydrogen and oxygen molecules are equal, we can write: Simplifying for the given molecular weights and temperatures, we find: Substituting the given values: Solving for : Thus, the temperature is 40 K.