Gas at a pressure of 0.85 bar, volume 0.25m^3 and temperature 18°c, is compressed until the pressure is 2.8 bar and volume is 0.115m^3, calculate the compression index and the final temperature.

n=1.53

T₂ = 166.16 °C

Explanation:

Given that

P₁=0.85 bar

V₁= 0.25 m³

P₂=2.8 bar

V₂=0.115  m³

Lets take compression index is n

So

Now by putting the values

ln 3.29 = n ln 2.17

n=1.53

T₁=18°C=273+ 18 = 291 K

Lets final temperature =T₂

T₂=439.16 K

T₂ = 166.16 °C

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .