Before a trip from New York to Boston, the pressure in an automobile tire is 2.5 atm at 272 K. At the end of the trip, the pressure gauge reads 1.94 atm. What is the new Celsius temperature of the air inside the tire?
(Assume tires with constant volume.)
Answer in units of degrees C
(P1/T1) = (P2/T2)
Remember T must be in kelvin.
i'm still not sure how to do this one. i've tried a couple of ways but it's been the wrong answer so far.
Type your work.
this is one way i did it..
2.5/272=1.94/?
.009?=1.94
?=215.6
Set up is right.
Algebra is ok except you rounded the 2.5/272 too much. Why did you throw the other numbers away?
2.5/272 = 0.00919 (I know that's too many places in my answer but I routinely carry one more than allowed, then round at the end). My best guess is that you are off just enough that 216 is not close enough.. By the way, if the 2.5 is the problem (and not 2.50) then 2 s.f. is all you are allowed.
As an extra note, I wouldn't believe this problem at all. When you drive from New York to Boston, the temperature goes UP in a tire and not down and pressure goes UP and not down.
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the volume of the tire is constant, we can rearrange the equation to solve for temperature:
T = PV / nR
First, we need to determine the initial temperature of the air inside the tire. We are given the initial pressure (P₁ = 2.5 atm) and temperature (T₁ = 272 K).
Next, we need to find the number of moles of gas inside the tire. Since the volume is constant, the number of moles remains the same before and after the trip.
Now, we can calculate the final temperature (T₂) using the ideal gas law. We are given the final pressure (P₂ = 1.94 atm).
Let's calculate the initial temperature (T₁) and then use it to find the new Celsius temperature of the air inside the tire.
To convert the initial temperature from Kelvin (K) to Celsius (°C), we need to subtract 273.15 from the temperature in Kelvin.
T₁ in °C = T₁ in K - 273.15
Plug in the given values:
T₁ in °C = 272 K - 273.15 = -1.15 °C
Now, using the ideal gas law, let's solve for the final temperature (T₂):
T₂ = (P₂ * V) / (n * R)
Since the volume (V), number of moles (n), and the ideal gas constant (R) are constant, we can simplify the equation to:
T₂ = P₂ * (V / (n * R))
Now, substitute the values:
T₂ = 1.94 atm * (V / (n * R))
Since V / (n * R) is constant, we can replace it with a single variable, C.
T₂ = 1.94 atm * C
Now, let's convert the final temperature (T₂) from Kelvin (K) to Celsius (°C).
T₂ in °C = T₂ in K - 273.15
Plug in the values:
T₂ in °C = (1.94 * C) - 273.15
Therefore, the new Celsius temperature of the air inside the tire is (1.94 * C) - 273.15.