The pressure in an automobile tire is 1.89 atm at 24.0°C. What will be the pressure if the temperature increases to 38.0°C?
i alreaddy got 1.89/24.0. i dont know where to go from there
the pressure is proportional to the absolute (Kelvin) temperature
1.89 / (24.0 + 273) = p / (38.0 + 273)
To continue solving this problem, we need to use the ideal gas law, which states:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
To solve for the new pressure, we need to convert the temperatures from Celsius to Kelvin:
T1 = 24.0°C + 273.15 = 297.15 K (initial temperature)
T2 = 38.0°C + 273.15 = 311.15 K (final temperature)
Since pressure and volume remain constant for this problem, we can rewrite the ideal gas law as:
P1/T1 = P2/T2
Now, we can plug in the values we already have:
P1 = 1.89 atm
T1 = 297.15 K
T2 = 311.15 K
Plugging these values into the equation, we can solve for P2:
P2 = P1 * (T2 / T1)
P2 = 1.89 atm * (311.15 K / 297.15 K)
To find the new pressure, simply calculate this expression:
P2 = 1.98 atm (rounded to two decimal places)
Therefore, the pressure in the automobile tire will be approximately 1.98 atm when the temperature increases to 38.0°C.
To solve this problem, you need to use the combined gas law equation. The combined gas law relates the pressure, volume, and temperature of a gas.
The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures, respectively,
V1 and V2 are the initial and final volumes, respectively,
T1 and T2 are the initial and final temperatures, respectively.
In this case, you know the initial pressure (P1 = 1.89 atm) and temperature (T1 = 24.0°C). You want to find the final pressure (P2) when the temperature increases to 38.0°C.
Since you are only interested in the pressure, you can isolate the P2 variable in the equation by rearranging it:
P2 = (P1 * V1 * T2) / (V2 * T1)
However, you need to make sure the temperatures are in Kelvin because temperature must be in Kelvin for gas laws calculations.
To convert Celsius to Kelvin, you can use the formula:
T(K) = T(°C) + 273.15
Now, let's plug in the values:
P1 = 1.89 atm
V1 (volume) is not given, so we can consider it constant.
T1 = 24.0°C + 273.15 = 297.15 K (converted to Kelvin)
T2 = 38.0°C + 273.15 = 311.15 K (converted to Kelvin)
P2 = (1.89 atm * V1 * 311.15 K) / (V2 * 297.15 K)
Since the volume is not given and it is not changing, you can cancel it out from the equation, leaving you with:
P2 = (1.89 atm * 311.15 K) / 297.15 K
Now evaluate the expression using a calculator to find the final pressure.