Ideal Gas Law Application: Propane Tanks Scenario
How can we determine the final pressure in the propane tanks?
Given two propane tanks with different initial conditions, how can we calculate the final pressure when they come to a uniform state?
Final Answer:
The final pressure in the propane tanks can be found using the ideal gas law equation.
Explanation:
The situation described in the question is an application of the ideal gas law, which states that PV = nRT. Here, P is pressure, V is volume, n is the number of moles of the gas, R is the universal gas constant, and T is temperature. In this case, since the amount of gas and the gas constant remain the same, we can write the equation for each tank as: P1V1 / T1 = P2V2 / T2.
For the first tank, we have: 150 kPa * 1 m3 / 300K = P2 * 1 m3 / 320K. For the second tank, we have: 250 kPa * 0.5 m3 / 380K = P2 * 0.5 m3 / 320K. Sum these two equations to find the final pressure (P2). The solution to these equations gives us the final pressure when the tanks come to a uniform state at 320K.
When dealing with scenarios involving gas tanks and pressure, understanding the ideal gas law can provide valuable insights. The ideal gas law equation, PV = nRT, encapsulates the relationship between pressure, volume, temperature, and the quantity of gas in moles.
In the context of the given data, the initial conditions of the two propane tanks are provided along with the final uniform state temperature. By applying the ideal gas law equation separately to each tank and then combining the equations, we can solve for the final pressure.
It is essential to remember that in this scenario, the amount of gas and the gas constant remain constant throughout the process. This allows us to simplify the calculations and focus on the pressure-volume-temperature relationships.
By substituting the initial and final conditions into the ideal gas law equation for each tank and solving the resulting equations, we can determine the final pressure of the propane tanks when they reach a uniform state at 320K.
Understanding and applying fundamental principles of thermodynamics, such as the ideal gas law, not only helps solve specific problems like this propane tank scenario but also lays a solid foundation for dealing with various gas-related challenges in physics and engineering.