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 the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature. The formula for the ideal gas law is:
P₁/T₁ = P₂/T₂
Where:
P₁ - initial pressure
T₁ - initial temperature (in Kelvin)
P₂ - final pressure
T₂ - final temperature (in Kelvin)
First, let's convert the initial temperature from Celsius to Kelvin. The equation to convert Celsius to Kelvin is:
T(K) = T(°C) + 273.15
Therefore, the initial temperature in Kelvin (T₁) is:
T₁ = 10 + 273.15 = 283.15 K
Next, let's plug in the given values into the ideal gas law equation:
325 kPa / 283.15 K = P₂ / 323.15 K
Now, let's solve for P₂, the final pressure:
P₂ = (325 kPa / 283.15 K) * 323.15 K
P₂ ≈ 371.46 kPa
Therefore, the new pressure of the tire, when the temperature rises to 50 degrees Celsius, is approximately 371.46 kPa.
To find the new pressure of the tire, we can use the ideal gas law equation:
P₁V₁/T₁ = P₂V₂/T₂
Where:
P₁ = initial pressure of the tire
V₁ = volume of the tire (given as constant)
T₁ = initial temperature of the tire in Kelvin
P₂ = new pressure of the tire (to be found)
V₂ = volume of the tire (given as constant)
T₂ = new temperature of the tire in Kelvin
First, let's convert the initial temperature of the tire from Celsius to Kelvin:
T₁ = 10 + 273.15 = 283.15 K
Next, let's convert the new temperature of the tire from Celsius to Kelvin:
T₂ = 50 + 273.15 = 323.15 K
Now, we can substitute the given values into the ideal gas law equation and solve for P₂:
P₁V₁/T₁ = P₂V₂/T₂
Since the volume of the tire is constant (V₁ = V₂), we can simplify the equation to:
P₁/T₁ = P₂/T₂
Substituting the values:
325 kPa / 283.15 K = P₂ / 323.15 K
Now, solve for P₂:
P₂ = (325 kPa * 323.15 K) / 283.15 K
P₂ ≈ 369.17 kPa
Therefore, the new pressure of the tire is approximately 369.17 kPa when the temperature rises to 50 degrees Celsius.