Thermodynamic- Internal energy of dry air

[harman12345]

Homework Statement

a) what is the density of dry air when the surface pressure is 1010hPa and the temperature is 27°C.

b) what is the internal energy of 1kg of dry air under these conditions?

Homework Equations

P=p*R*T where P is pressure and p is density.

The Attempt at a Solution

a) p = RT/P by solving it gives me
[287*(273+27)] / 101000 => 0.852kg/m

can someone please check what i did for part (a) is right or not?

b) i don't really get where to go with this question. So some help would be really appreciated thanks!

 

[ehild]

Homework Equations

P=p*R*T where P is pressure and p is density.

The Attempt at a Solution

a) p = RT/P

Think it over...

ehild

 

[harman12345]

Think it over...

ehild

OH my bad! should be p=P/RT right?

and hint for part b please

 

[ehild]

The internal energy of the ideal gas is the kinetic energy -both translational and rotational- of its molecules. You must have learned about it. For an ideal gas, it is U=c_vmT, where c_v is the specific heat capacity at constant volume.

http://www.ohio.edu/mechanical/thermo/property_tables/air/air_Cp_Cv.htmlehild

 

[asteriatic]

I can confirm that your calculation for the density of dry air at a surface pressure of 1010hPa and temperature of 27°C is correct.

For part (b), the internal energy of a substance is the sum of its kinetic and potential energies at the molecular level. In other words, it is the total energy contained within the molecules of the substance. The internal energy of 1kg of dry air can be calculated using the following equation:

U = m * u * n

where U is the internal energy, m is the mass of the substance (1kg in this case), u is the specific internal energy (J/kg) and n is the number of moles of the substance.

To find u, we can use the thermodynamic equation:

u = Cv * T

where Cv is the specific heat capacity at constant volume and T is the temperature. For dry air, Cv is approximately 0.718 kJ/kgK.

Therefore, the internal energy of 1kg of dry air at a temperature of 27°C can be calculated as:

U = (1kg) * (0.718 kJ/kgK) * (300K) = 215.4 kJ

I hope this helps! Let me know if you have any other questions.