Final answer:
The final pressure after adiabatic expansion can be found using the adiabatic condition formula. Assuming an initial pressure at NTP and using the specific heat ratio for air, the final pressure can be calculated when the volume expands to five times the original volume.
Step-by-step explanation:
To calculate the final pressure after adiabatic expansion of air, we can use the adiabatic condition which states that PVγ is a constant, where P is the pressure, V is the volume, and γ (gamma) is the specific heat ratio. As the volume expands to five times the original volume under adiabatic conditions, we must assume no heat is added or removed from the system. The initial condition is described by PoVoγ, and the final condition by PfVfγ. By setting these two expressions equal to each other and solving for the final pressure Pf, we obtain an equation of the form:
Pf = Po×(ðo/Vf)γ
Since the specific heat ratio for air is given as 1.4, and the volume expands by a factor of 5, the equation simplifies to:
Pf = Po×(1/5)1.4
Substitute the known value of Po (initial pressure at NTP, which is 1.01325×105 Pa) into the equation to find Pf, the final pressure.