Calculating Heat Needed to Raise Room Temp: An Ideal Gas Approach

[FahimP]

Homework Statement

Treating air as an ideal gas of diatomic molecules, calculate how much heat is required to raise the temperature of the air in an 8.3 m by 13 m by 5.0 m room from 24 °C to 27 °C at 101 kPa.

Homework Equations

PV = nRT ---> n = PV/RT
Q = NCpDeltaT

The Attempt at a Solution

I am using PV = nRT to solve for n

then I am using Q = nCPdeltaT
where CP is constant pressure of air 29.4

any help what am i doing wrong

 

[lippyka]

here?P = 101 kPaV = 8.3 m x 13 m x 5.0 m = 459.5 m^3R = 8.314 J/molKT = 24 Celsius + 273.15 K = 297.15KdeltaT = 27C - 24C = 3Cn = (101 x 459.5)/(8.314 x 297.15) = 1.75 molQ = 1.75 x 29.4 x 3 = 158.5 J