In the virtual lab demo, a student adds particles to a container. While the volume is held constant the initial temperature of the container is 300K.

Question

The pressure fluctuates around what amount?

The student adds heat to the container with the particles. What part of the lab changes?

When the temperature is lowered to half its temperature (150K), the pressure
to about
the original pressure. The new pressure is now about:
.

You can predict, if the temperature was increased 4x the initial temperature, then the pressure would
to
the original pressure.

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Answer 1

In the scenario you described, we can apply the ideal gas law, which states that \( PV = nRT \), where:

• \( P \) is the pressure of the gas,
• \( V \) is the volume,
• \( n \) is the number of moles of gas (which remains constant as particles are added),
• \( R \) is the ideal gas constant,
• \( T \) is the temperature in Kelvin.

Here’s how we can break it down:

1. Initial Conditions:

   • The volume is constant, and the initial temperature is 300 K.
   • The pressure will fluctuate around some value, \( P_1 \), which we cannot determine without additional information, but we'll consider it a baseline pressure.

2. When Heat is Added:

   • Adding heat to the container will increase the temperature of the gas. Since the volume is held constant, the pressure will increase as a result of the increased kinetic energy of the particles.

3. Lowering Temperature:

   • When the temperature is lowered to half its initial value (150 K), according to the ideal gas law, if the volume and the number of particles remain constant, the new pressure \( P_2 \) can be determined by the ratio of the temperatures: \[ P_2 = P_1 \times \frac{T_2}{T_1} = P_1 \times \frac{150 K}{300 K} = 0.5 P_1 \] Thus, the new pressure is about half the original pressure.

4. Predicting Pressure with Increased Temperature:

   • If the temperature is increased to four times the original temperature (4 × 300 K = 1200 K), then: \[ P_3 = P_1 \times \frac{T_3}{T_1} = P_1 \times \frac{1200 K}{300 K} = 4 P_1 \] Therefore, the pressure would rise to four times the original pressure.

To summarize:

• The pressure fluctuates around \( P_1 \).
• When heat is added, the pressure increases due to increased kinetic energy.
• The new pressure at 150 K is about \( 0.5P_1 \).
• If the temperature is increased to 1200 K, the pressure would rise to \( 4P_1 \).

Answer 2

can you give me the answer in sentences

Answer 3

Sure! Initially, the pressure in the container fluctuates around a certain value, which we can refer to as \( P_1 \). When the student adds heat to the container, the pressure increases due to the increased kinetic energy of the particles while the volume remains constant.

As the temperature is lowered to 150 K, which is half of the initial temperature of 300 K, the new pressure reduces to about half of the original pressure, making it approximately \( 0.5 P_1 \).

Additionally, if the temperature is increased to four times the initial temperature (1200 K), the pressure would rise to four times the original pressure, resulting in a new pressure of \( 4 P_1 \).