# Calculating virtual temperature

1. Apr 27, 2013

### Timebomb3750

1. The problem statement, all variables and given/known data
Problem: On a summer day, your classroom warms and becomes muggy with a vapor pressure of 20hPa and a temperature of 25C.

a.) If the volume of the classroom is 40m^3, how much water is present in the room in vapor form?Assume density of liquid water is 1000 kg/m^3

b.) If the pressure in the room is 900hPa, what is the virtual temperature?

2. Relevant equations

Ideal gas laws: e=(m/v)RT ; P=ρ(Rd)Tv

3. The attempt at a solution

Finding the answer to part a.) was easy. I used the ideal gas law e=(m/v)RT and solved for m. The answer I got was .58kg, and that's correct. What I'm having a hard time with is part b.). I figured you could just use another form of the ideal gas law P=ρ(Rd)Tv, where Rd is the gas constant for try air, ρ is density, and Tv is the virtual temperature. So I set up my formula like this:

90,000 N/m^2 = (1000 kg/m^3)*(287 J/kg*K)*Tv

I converted the 900hPa into Pascals and then expressed Pascals as Newtons per square meter.

When I solve for Tv, I strangely get .314 K. I know this isn't right as the answer is supposed to be 300.7 K. So, what am I doing wrong here?

2. Apr 27, 2013

### FireStorm000

Isn't the density of air only about one kilogram per cubic meter, rather than one tonne? That would explain why you're off by about a factor of 1000.