Answer
1550 watts.
Work Step by Step
The heater heats 130 cubic meters of air per hour from $5^{\circ}$ to $22^{\circ}$.
Use equation 14–2 to calculate the energy needed to heat the air.
$$Q=mc\Delta T$$
$$\frac{Q}{t}=\frac{m}{t}c \Delta T=\frac{130m^3}{3600s}\frac{1.29kg}{m^3}\frac{0.17kcal}{kg \cdot C^{\circ}}(17C^{\circ})=0.1346kcal/s$$
The heater also replaces the heat that is being lost (850 kcal/h, or 0.2361 kcal/s). Calculate the total required power.
$$(0.1346kcal/s+0.2361 kcal/s)\frac{4186J}{kcal}\approx 1550W$$
