Help with flow speed & Thermodynamics

I have 2 questions that I need help with:

1. a room measures 3m by 4.5m by 6m. The heating and air conditioning ducts to and from the room are cicular witha a diameter of 0.30m, and the air in the room is to be exchanged every 12 minutes. What is the necessary flow speed in the duct? (assume that the disity of the airs is constant)

2. A house has well-insulated walls. It contains a volume of 100 m^3 of air at 300K. Calculate the energy ot increase the temperature of this diatomic gas by 2 degrees C. Assume it is heating at a constant pressure and use Cp=7R/2.

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For the first problem, the air ducts must remove (and replenish) a volume of air given by 3m x 4.5m x 6m in 12 min. Thus the mass flow rate of the system is given by

$$\frac{dm}{dt} = \rho \frac{dV}{dt} = \frac{\rho_{air} V}{t} = \rho_{air} \frac{3\cdot 4.5\cdot 6 \ meters^3}{12 \ min}$$

Of course you'll have to convert minuntes to seconds to get a flow rate of kg/s. You can use the same formula to calculate the flow speed in the air duct like so.

$$\frac{dm}{dt} = \rho \frac{d(AL)}{dt} = \rho A \frac{dL}{dt} = \rho A v$$

Here, A is the cross sectional area of the pipe and v is the velocity that you're looking for.

For the second problem use

$$C_p = \frac{7}{2} nR = \frac{\partial U}{\partial T}$$

Here, n is the number of moles of the gas (you can determine this from the ideal gas law) and C_p is the HEAT CAPACITY (not specific heat) at constant pressure.