To what temperature must a sample of helium gas be cooled from 110 degrees C to reduce its volume from 4.9 L to 0.7 L at constant pressure?
Answer in units of K
(V1/T1) = (V2/T2)
To find the temperature at which the sample of helium gas must be cooled, we can use the combined gas law equation:
P1V1/T1 = P2V2/T2
Where:
P1 = initial pressure (assumed constant)
V1 = initial volume
T1 = initial temperature in Kelvin
P2 = final pressure (assumed constant)
V2 = final volume
T2 = final temperature in Kelvin
Given:
P1 = P2 (constant pressure)
V1 = 4.9 L
V2 = 0.7 L
First, we need to convert the initial temperature from degrees Celsius to Kelvin:
T1 (in Kelvin) = T1 (in Celsius) + 273.15
T1 = 110 °C + 273.15
T1 = 383.15 K
Using the combined gas law equation, we can rearrange it to solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Substituting the given values:
T2 = (P2 * V2 * T1) / (P1 * V1)
T2 = (1 * 0.7 * 383.15) / (1 * 4.9)
T2 = 26.795 K
Therefore, the sample of helium gas must be cooled to approximately 26.795 K in order to reduce its volume from 4.9 L to 0.7 L at constant pressure.
To solve this problem, we need to use the combined gas law formula, which relates the initial and final temperatures and volumes of a gas sample at constant pressure.
The combined gas law formula is:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature in Kelvin
P2 = final pressure (given as constant)
V2 = final volume
T2 = final temperature in Kelvin (unknown)
Given values:
P1 = P2 (constant pressure)
V1 = 4.9 L
V2 = 0.7 L
T1 = 110°C (initial temperature in Celsius)
First, we need to convert the initial temperature from Celsius to Kelvin. To convert Celsius to Kelvin, we add 273.15 to the Celsius value.
T1 = 110°C + 273.15 = 383.15 K
Now we can rearrange the formula to solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Plug in the known values:
T2 = (P2 * V2 * T1) / (P1 * V1)
= (P2 * 0.7 L * 383.15 K) / (P1 * 4.9 L)
Since both P1 and P2 are given as constant, we can cancel them out:
T2 = (0.7 L * 383.15 K) / 4.9 L
Now, we can calculate T2:
T2 = (0.7 * 383.15) / 4.9 ≈ 54.688
Therefore, the sample of helium gas must be cooled to approximately 54.688 K to reduce its volume from 4.9 L to 0.7 L at constant pressure.