An automobile tire has a pressure of 325 kPa when the temperature is 10 degrees Celsius. If the temperature of the tire rises to 50 degrees Celsius and its volume is constant,what is the new pressure?
To find the new pressure of the tire, we can use Charles's law, which states that the pressure of a gas is directly proportional to its temperature when the volume is constant.
According to Charles's law, we can calculate the new pressure using the following formula:
P₁/T₁ = P₂/T₂
Where:
P₁ = Initial pressure of the tire
T₁ = Initial temperature of the tire
P₂ = New pressure of the tire (what we need to find)
T₂ = New temperature of the tire
Given:
P₁ = 325 kPa
T₁ = 10 degrees Celsius = 10 + 273.15 = 283.15 K
T₂ = 50 degrees Celsius = 50 + 273.15 = 323.15 K
Now, let's substitute these values into the formula and solve for P₂:
325 kPa / 283.15 K = P₂ / 323.15 K
Simplifying the equation:
P₂ = (325 kPa × 323.15 K) / 283.15 K
P₂ ≈ 370.23 kPa
Therefore, the new pressure of the tire when the temperature rises to 50 degrees Celsius is approximately 370.23 kPa.
To find the new pressure of the automobile tire when the temperature rises to 50 degrees Celsius, we can use the ideal gas law.
The ideal gas law is represented as:
PV = nRT
Where:
P = Pressure (in Pascals)
V = Volume (in cubic meters)
n = Number of moles
R = Gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale does not use negative values.
T(K) = T(°C) + 273.15
Initial temperature (T1) = 10°C + 273.15 = 283.15 K
Final temperature (T2) = 50°C + 273.15 = 323.15 K
Since the volume is constant, V1 = V2.
Now, let's rearrange the ideal gas law equation to solve for pressure:
P1/T1 = P2/T2
Substituting the given values, we have:
325 kPa / 283.15 K = P2 / 323.15 K
Now, we can solve for P2:
P2 = (325 kPa * 323.15 K) / 283.15 K
P2 ≈ 371.37 kPa
Therefore, the new pressure of the automobile tire when the temperature rises to 50 degrees Celsius is approximately 371.37 kPa.
4x10^2 KPa
P V = n R T
here
V, n and R are constant so
P1/T1 = P2/T2
Pi = 325 k Pa
T1 = 10 + 273 = 283
T1 = 50 + 273 - 323
P2 = P1 T2/T1