Imagine that a deposit of helium gas has been discovered in Antarctica. It is being shipped to Australia in a rigid (constant volume) tank with a rated max pressure of 100 atm. If the tanks are filled to a pressure of 75 atm in Antarctica on a day when the temp is -100F, will the pressure be within the safety limits if the tanks arrive in Australia on a day when the temp is 90F? Need to show calculations...
Convert -100 F and 90 F to celsius, then to Kelvin
Then use (P1V2)/T1 = (P2V2)/T2
Solve for P2.
To determine whether the pressure in the tanks will be within the safety limits when the tanks arrive in Australia, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas (constant in this case)
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
First, let's convert the temperatures to Kelvin:
-100 degrees Fahrenheit = (-100 + 459.67) degrees Rankine
90 degrees Fahrenheit = (90 + 459.67) degrees Rankine
Since Rankine is the Fahrenheit temperature scale adjusted to absolute zero, it can be used directly in the ideal gas law equation.
Now, let's determine the ratio of pressures using the ideal gas law:
(P1 * V) / T1 = (P2 * V) / T2
Simplifying the equation by canceling out the volume:
P1 / T1 = P2 / T2
Substituting the given values:
P1 = 75 atm
T1 = -100 + 459.67 = 359.67 Rankine
P2 = ?
T2 = 90 + 459.67 = 549.67 Rankine
Now we can solve for P2:
P2 = (P1 * T2) / T1
P2 = (75 atm * 549.67 Rankine) / 359.67 Rankine
Calculating the value of P2:
P2 = 113.54 atm
Now we can compare P2 to the maximum rated pressure of the tank, which is 100 atm. Since P2 is greater than 100 atm, the pressure will exceed the safety limits if the tanks arrive in Australia on a day with a temperature of 90 degrees Fahrenheit.
Therefore, the pressure will not be within the safety limits.