A tyre is suddenly brust when it was pumped to a presure of 4 atm at 20 degree celsius. Calculate the final temperature.
To calculate the final temperature, we can use the ideal gas law equation, which relates the pressure, volume, temperature, and number of gas particles in a system:
PV = nRT
Where:
P = pressure
V = volume
n = number of particles (in moles)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature
In this case, the volume and number of gas particles remain constant, so we can simplify the equation to:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature
We are given the initial pressure (4 atm) and temperature (20 °C), and we need to find the final temperature.
First, let's convert the initial temperature from Celsius to Kelvin:
T1(K) = T1(°C) + 273.15
= 20 + 273.15
= 293.15 K
Now, rearranging the equation, we have:
T2 = (P2 * T1) / P1
Substituting the values, we get:
T2 = (1 * 293.15) / 4
= 73.29 K
Therefore, the final temperature is approximately 73.29 Kelvin.