Energy can be stored in compressed air through an isothermal or isentropic compression process. Assume that 1m3 of air has an initial state of 0.1MPa in pressure, 288k in temperature and 1.225 kg in mass. It is compressed to 2 MPa and then expanded back to the initial state to recover the energy.

Suppose that air is compressed and expanded through an isothermal process (V=constant)

How much are the final volume and temperature of the air after compression?

To find the final value of volume, we use the ideal gas equation,

As this is the case of ideal gas equation so the temperature is same or remains constant.

 How much energy is stored

No energy is stored.

How much is the corresponding energy storage density value?

Suppose that air is compressed and expanded through an isentropic process  

How much are the final volume and temperature of the air after compression?

How much energy is stored

Where K is the stefhen constant

How much is the corresponding energy storage density value?

Compare the above two values of energy storage density and explain the difference.

In isothermal energy storage density the temperature is constant and according to the ideal gas law pressure is proportional to the density simply in contrast isentropic is the adiabatic reversible process.

In another solar system, there is a star having a surface temperature of 5000 degree and a radius of 5*105 km. A planet orbits the star at a distance of 1.6108km. The planet has a cloudless atmosphere such that, for an air mass of 1, the clearness index is constantly 0.65. just above its atmosphere, a satellite orbits the planet once every 72 hours and carries a photovoltaic panel of area 2m2 and efficiency 13%. Throughout the orbit of the satellite, the panel remains horizontal with respect to the surface of the planet directly below it. as shown in the diagram, the orbit of the satellite is circular and lies in a plane that includes a line drawn between  the centre of the star and the centre of planet.

Work out the ‘solar constant’ for the planet

Work out the irradiance at the surface of the planet when the sun is directly overhead.

Solution

Temperature of 5000 degree

Radius of 5*105 km

Distance of 1.6108km

Clearness index is constantly 0.65.

Time= 72 hours

Efficiency 13%.

According to Boltz constant

Solar constant= 

Whereas sigma is constant    

Solar constant=

On the give day the simplified equation for irradiance is

On decades as well as longer timescales total solar irradiance changes slowly. The difference throughout solar cycle 21 was regarding 0.1%.

Here is the graph of photovolatic panel against time

We know that the 12 volt natural battery delivers the 48 ampere of current it means that for 48 hours battery use only one ampere. So,

Due to the 100% efficiency

We know that power is equal to the product of current and voltage

P=VI

P=(12)*(48)

P=576 Watt

5)

Now we want to find the value of the capacity of the battery

As we know the battery ampere is 48 and amperes

So;