Two ideal gases have the same mass density and the same absolute pressure. one of the gases is helium (he), and its temperature is 175 k the other gas is neon (ne). what is the temperature of the neon?

Temperature of neon gas = 875 K

Explanation:

Using Ideal gas equation as:

PV=nRT

Where,

P is the pressure of the gas

V is the volume of the gas

n is the number of moles

R is the gas constant

T is the temperature

Also,

The ideal gas equation can be written as:

Thus,

As Density and Pressure is constant , We only consider molar mass and Temperature which are directly proportional according to the equation above as:

Data given for He:

Temperature (T₁) = 175 K

Molar mass of He (M₁)= 4 g/mol

For Ne:

Temperature (T₂)= ?

Molar mass of He (M₂)= 20 g/mol

Applying in the equation,

Temperature of neon gas = 875 K

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 .