Answer:
To calculate the temperature to which a 1.0L sample of perfect gas can be cooled from 25⁰C in order to reduce its volume to 100cm³, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas
In this case, we are given that the initial volume (V1) is 1.0L and the final volume (V2) is 100cm³. We need to find the final temperature (T2) when the initial temperature (T1) is 25⁰C.
First, we need to convert the volumes to a consistent unit. Since 1L = 1000cm³, we have V1 = 1000cm³ and V2 = 100cm³.
Next, we can rearrange the ideal gas law equation to solve for T2:
T2 = (P2 * V1 * T1) / (P1 * V2)
Since it is not specified, we assume that the pressure remains constant during this process. Therefore, P1 = P2.
Substituting the given values into the equation:
T2 = (P * 1000cm³ * 25⁰C) / (P * 100cm³)
The pressure cancels out, leaving us with:
T2 = (1000cm³ * 25⁰C) / 100cm³
Simplifying further:
T2 = 25000⁰C / 100cm³
T2 = 250⁰C
Therefore, in order to reduce the volume of a 1.0L sample of perfect gas from 25⁰C to 100cm³, the temperature needs to be cooled to 250⁰C.
Step-by-step explanation: