Answer
The ideal gas model can be applied to the final state, state 2, to determine the temperature of the
air remaining in the tank.
$p_{2}$$V_{2}$ = $m_{2}$R$T_{2}$
Solving for temperature yields
$T_{2}$=$m_{2}$ R/$p_{2}$ $V_{2}$
Pressure and volume are known at state 2. The mass in the tank at state 2, $m_{2}$, equals the initial mass in the tank, $m_{1}$, less the mass that leaks from the tank. Since the mass flow rate, is 0.03 lb/sec
constant, the amount of mass that leaks from the tank is
mass flow rate * t = (0.03 lb/s)(90 s) = 2.7 lb
The initial mass, m1, is obtained using the ideal gas equation of state
$m_{1}$ =($p_{1}$$V_{1}$)/(R$T_{1}$).
The R here is universal gas constant divided by molecular mass of air.
Temperature must be expressed on an absolute scale, T1 = 80 degree F = 540 degree R. Substituting values
and applying the appropriate conversion factor yield
$m_{1}$= 4.0 lb.
Collecting results
$m_{2}$ = 4.0 lb – 2.7 lb = 1.3 lb
Substituting m2 to solve for T2 yields
$T_{2}$ = 498.5 degree R = 38.5 degree F.
Work Step by Step
The ideal gas model can be applied to the final state, state 2, to determine the temperature of the
air remaining in the tank.
$p_{2}$$V_{2}$ = $m_{2}$R$T_{2}$
Solving for temperature yields
$T_{2}$=$m_{2}$ R/$p_{2}$ $V_{2}$
Pressure and volume are known at state 2. The mass in the tank at state 2, $m_{2}$, equals the initial mass in the tank, $m_{1}$, less the mass that leaks from the tank. Since the mass flow rate, is 0.03 lb/sec
constant, the amount of mass that leaks from the tank is
mass flow rate * t = (0.03 lb/s)(90 s) = 2.7 lb
The initial mass, m1, is obtained using the ideal gas equation of state
$m_{1}$ =($p_{1}$$V_{1}$)/(R$T_{1}$).
The R here is universal gas constant divided by molecular mass of air.
Temperature must be expressed on an absolute scale, T1 = 80 degree F = 540 degree R. Substituting values
and applying the appropriate conversion factor yield
$m_{1}$= 4.0 lb.
Collecting results
$m_{2}$ = 4.0 lb – 2.7 lb = 1.3 lb
Substituting m2 to solve for T2 yields
$T_{2}$ = 498.5 degree R = 38.5 degree F.
