Thermodynamic- Internal energy of dry air

In summary, the conversation discusses the density of dry air at a surface pressure of 1010hPa and temperature of 27°C, as well as the internal energy of 1kg of dry air under these conditions. The equation P=p*R*T is used to calculate the density in part (a), and the specific heat capacity at constant volume (cv) is mentioned as a hint for part (b) in finding the internal energy.
  • #1
harman12345
2
0

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!
 
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  • #2
harman12345 said:

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
 
  • #3
ehild said:
Think it over...

ehild

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

and hint for part b please
 
  • #4
Last edited:
  • #5


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.
 

Related to Thermodynamic- Internal energy of dry air

1. What is the definition of internal energy in thermodynamics?

Internal energy in thermodynamics is the total energy contained within a system, including both its kinetic and potential energies. It is a measure of the microscopic energy of a system's particles and is affected by factors such as temperature, pressure, and composition.

2. How is internal energy related to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

3. How does the internal energy of dry air differ from other substances?

Dry air, or air that does not contain any water vapor, has a lower internal energy compared to other substances due to the lack of molecular interactions between its particles. This means that dry air requires less energy to change its temperature compared to substances with stronger intermolecular forces.

4. How does the internal energy of dry air affect its temperature?

The internal energy of dry air is directly related to its temperature. As the temperature of dry air increases, its internal energy also increases, and vice versa. This is because the kinetic energy of the air molecules, which is a component of internal energy, increases with temperature.

5. Can the internal energy of dry air be measured?

Yes, the internal energy of dry air can be measured using various methods, such as calorimetry or thermodynamic equations. By measuring the temperature and pressure of dry air, its internal energy can be calculated using the ideal gas law or other thermodynamic equations.

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