A piston is used to compress a gas from 1.0 atm to 3.5 atm. If ther volume changes from 1.5L to 0.75L, what is the final temperature, if it started at 300k?
1050K
700K
525K
300K
Use (P1V1/T1) = (P2V2/T2)
525K
Thank you!
Good
To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
Since we are given the initial and final pressures (P1 = 1.0 atm and P2 = 3.5 atm), the initial volume (V1 = 1.5 L), and the initial temperature (T1 = 300 K), we can use the ideal gas law equation for the initial state:
P1V1 = nRT1
Now, let's find the value of nRT1 by rearranging the equation:
nRT1 = P1V1
Next, we need to find the number of moles of gas (n) in order to determine the final temperature (T2). We can use the equation n = PV/RT to calculate it.
First, let's find the value of n using the initial conditions:
n = (P1V1) / (RT1)
Substituting the given values, we have:
n = (1.0 atm * 1.5 L) / (0.0821 L·atm/(mol·K) * 300 K)
n = 0.06 mol
Now, we can determine the final temperature (T2) using the ideal gas law equation for the final state:
P2V2 = nRT2
Rearranging the equation to solve for T2, we have:
T2 = (P2V2) / (nR)
Substituting the given values, we get:
T2 = (3.5 atm * 0.75 L) / (0.06 mol * 0.0821 L·atm/(mol·K))
T2 ≈ 1050 K
Therefore, the final temperature (T2) is approximately 1050 K.
So, the correct answer is 1050K.