Which temperature change would cause the volume of a sample of an ideal gas to double when the pressure of the sample remains the same?

1. from 200°C to 400°C
2. from 400°C to 200°C
3. from 200K to 400K
4. from 400K to 200K

3. from 200K to 400K

Hello random people in the future. :-)

im still here for test answers lol

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06/15/22

To determine the temperature change that would cause the volume of an ideal gas to double while keeping the pressure constant, we need to apply Charles' Law.

Charles' Law states that at constant pressure, the volume of a given amount of gas is directly proportional to its temperature. Mathematically, it can be expressed as:

V1/T1 = V2/T2

Where V1 and V2 are the initial and final volumes respectively, and T1 and T2 are the initial and final temperatures respectively.

In our case, since we want the volume to double, we can assume that the initial volume (V1) is 1 and the final volume (V2) is 2. Furthermore, since we want to keep the pressure constant, we can use the equation as follows:

1/T1 = 2/T2

Now, we can analyze each option and see which one satisfies the equation.

1. From 200°C to 400°C:
To use the equation, we need to convert the temperatures to Kelvin since the Kelvin scale is based on absolute zero.
T1 = 200°C + 273.15 = 473.15K
T2 = 400°C + 273.15 = 673.15K

Plugging in the values:
1/473.15 = 2/673.15
0.002113 = 0.002972

The equation is not satisfied, so Option 1 is not the correct answer.

2. From 400°C to 200°C:
T1 = 400°C + 273.15 = 673.15K
T2 = 200°C + 273.15 = 473.15K

Plugging in the values:
1/673.15 = 2/473.15
0.001487 = 0.004221

Again, the equation is not satisfied, so Option 2 is not the correct answer.

3. From 200K to 400K:
Here, the temperatures are already in Kelvin, so we don't need to convert them.

Plugging in the values:
1/200 = 2/400
0.005 = 0.005

The equation is satisfied, so Option 3 is the correct answer.

4. From 400K to 200K:
Plugging in the values:
1/400 = 2/200
0.0025 = 0.01

The equation is not satisfied, so Option 4 is not the correct answer.

Therefore, the correct answer is Option 3. A temperature change from 200K to 400K would cause the volume of a sample of an ideal gas to double, while keeping the pressure constant.

The volume is directly proportional to the KELVIN temperature (not Celsius).