A glass vessels contains air at 300K at what temperature must it be heated to expel one-fourth of the air, the pressure remaining constant?

To determine the temperature at which one-fourth of the air in a glass vessel must be expelled while keeping the pressure constant, we can use Charles's Law. This law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant. In this case, we need to find the new temperature after expelling a portion of the air.

Understanding the Problem

Initially, we have a certain volume of air at a temperature of 300 K. If we expel one-fourth of the air, we are left with three-fourths of the original volume. Since the pressure remains constant, we can set up a relationship using Charles's Law:

Charles's Law Formula

The formula can be expressed as:

• V1/T1 = V2/T2

Where:

• V1 = initial volume of the gas
• T1 = initial temperature (300 K)
• V2 = final volume of the gas (3/4 of V1)
• T2 = final temperature (unknown)

Setting Up the Equation

Since we know that V2 is three-fourths of V1, we can substitute into the equation:

V1 / T1 = (3/4)V1 / T2

Canceling Out Terms

We can simplify this equation by canceling V1 from both sides:

1 / T1 = (3/4) / T2

Solving for the Final Temperature

Now we can rearrange the equation to solve for T2:

T2 = (3/4) * T1

Substituting the Known Values

Now, plug in the initial temperature:

T2 = (3/4) * 300 K

T2 = 225 K

Final Thoughts

Thus, to expel one-fourth of the air while keeping the pressure constant, the temperature must be lowered to 225 K. This demonstrates how gas behavior is influenced by temperature and volume under constant pressure conditions, illustrating the principles of thermodynamics in a practical scenario.