High-pressure helium is available from gas producers in 0.045-m^3 cylinders at 400 bar and 298 K. Calculate the explosion equivalent of a tank of compressed helium in terms of kilograms of TNT. Assume helium is an ideal gas
To calculate the explosion equivalent of a tank of compressed helium in terms of kilograms of TNT, we need to find the amount of energy released by the compressed helium, and then compare it to the energy released by an equivalent amount of TNT.
First, let's calculate the number of moles of helium in the tank. We can use the ideal gas law equation:
PV = nRT, where P is the pressure in Pa, V is the volume in m^3, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature in Kelvin.
First, convert the pressure from bar to Pa:
1 bar = 100,000 Pa
So, 400 bar = 400 * 100,000 Pa = 40,000,000 Pa
Next, convert the volume from m^3 to liters:
1 m^3 = 1000 liters
So, 0.045 m^3 = 0.045 * 1000 liters = 45 liters
Now, let's calculate the number of moles (n):
PV = nRT
n = (PV) / (RT)
n = (40,000,000 Pa * 45 liters) / (8.314 J/(mol·K) * 298 K)
n ≈ 611.34 moles of helium
Now that we know the number of moles of helium, we can calculate the energy released by the compressed helium using the equation:
Energy = n * Cv * ΔT
Where n is the number of moles, Cv is the molar heat capacity at constant volume for helium (5/2 R), and ΔT is the change in temperature.
Since the temperature is constant, ΔT = 0 K.
Energy = n * (5/2 * R) * ΔT
Energy = n * (5/2 * R) * 0
Energy = 0
Since ΔT is zero, there is no energy released by the helium tank. Therefore, the explosion equivalent in terms of kilograms of TNT is zero.
Note: This result is expected as helium is a non-reactive gas and does not undergo explosive reactions like TNT.