# How long to heat a given volume of air?

## Homework Statement

I am working on a problem where I need to determine the time taken for an air heater with an 8kW output to heat a volume of air of 9m^3 by 25C. I am neglecting all losses at the moment. It almost seems too simple in my mind that I'm concerned I'm overlooking something.

## Homework Equations

cp = 1005 J kg-1 K-1
ρ = 1.534 kg m-3
Q = cp * m * dT

## The Attempt at a Solution

Q = 1005 * (1.534 * 9) * 25 = 346875.75 J = 0.35MJ

As 1kWh = 3.6MJ:

0.35 / 3.6 = 0.097kWh required for a dT of 25C to heat a 9m^3 volume of air.

The time required would therefore be 0.097 / 8 = 0.012 hours or approximately 43 seconds.

Am I along the right lines here?

jrmichler
Mentor
Yes, you got it right. It really is that easy when you understand what you are doing.

Just for grins and giggles, what is the pressure of that air assuming the temperature is 25 deg C?

evoke1l1
Thank you for confirming this.

I’m assuming the change in pressure over the 25C change?

This would be caluculated by p2 = (p1 * T2) / T1 I believe.