To determine the final pressure inside the tank after the temperature change, we can use the ideal gas law, which states:
PV = nRT
Where: P is the pressure V is the volume n is the number of moles of gas R is the ideal gas constant T is the temperature in Kelvin
In this case, we have the initial pressure (P1 = 30.0 kPa), the initial temperature (T1 = -100.0 °C), and the final temperature (T2 = 1.00 x 10^3 °C). We need to find the final pressure (P2).
First, let's convert the temperatures to Kelvin:
T1 = -100.0 °C + 273.15 = 173.15 K T2 = 1.00 x 10^3 °C + 273.15 = 1273.15 K
Since we are assuming the volume (V) and the number of moles (n) of gas remain constant, we can write the equation as:
P1/T1 = P2/T2
Now, we can substitute the known values into the equation:
30.0 kPa / 173.15 K = P2 / 1273.15 K
To solve for P2, we can rearrange the equation:
P2 = (30.0 kPa / 173.15 K) * 1273.15 K
Calculating the expression on the right-hand side:
P2 ≈ 221.34 kPa
Therefore, the final pressure inside the tank after the temperature change is approximately 221.34 kPa.