Calculate the mass of air in a closed system given initial volume, temperature, and pressure, and properties of air.

Step 1: Convert given values to SI units and define properties of air.
Given:
Initial volume, $V_1 = 1 \, \text{m}^3$
Initial temperature, $T_1 = 15^\circ\text{C} = 15 + 273.15 = 288.15 \, \text{K}$
Temperature after heating, $T_2 = 300^\circ\text{C} = 300 + 273.15 = 573.15 \, \text{K}$
Initial pressure, $P_1 = 1.03 \, \text{bar} = 1.03 \times 10^5 \, \text{Pa}$

For air (assumed ideal gas):
Specific heat at constant pressure, $c_p = 1.005 \, \text{kJ/kg}\cdot\text{K}$
Specific heat at constant volume, $c_v = 0.718 \, \text{kJ/kg}\cdot\text{K}$
Gas constant, $R = c_p - c_v = 1.005 - 0.718 = 0.287 \, \text{kJ/kg}\cdot\text{K} = 287 \, \text{J/kg}\cdot\text{K}$

Step 2: Calculate the mass of air ($m$).
Using the ideal gas law at state 1: $P_1 V_1 = m R T_1$

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