A water vapour thermometer is calibrated at the ice and steam points and the saturation

Question

A water vapour thermometer is calibrated at the ice and steam points and the saturation

vapour pressures (s.v.p) are measured. The saturation vapour pressure Pθ is given by
P  P01   2 , where P0 is the s.v.p at the ice point, θ is the temperature in ˚C on
the Celsius scale, α and β are constants and α = 40 β ˚C. Determine the temperature of a
medium on the water vapour scale if its temperature on the Celsius scale is 50 ˚C

Answer 1

To determine the temperature of a medium on the water vapor scale, we need to use the equation for the saturation vapor pressure Pθ on the Celsius scale.

The given equation for Pθ is:
Pθ = P0(1 + αθ + βθ^2)

We know that α = 40β, so we can rewrite the equation as:
Pθ = P0(1 + 40βθ + βθ^2)

To determine the temperature on the water vapor scale, we need to solve this equation for θ when the Celsius temperature is 50°C.

Let's substitute the given values into the equation:
Pθ = P0(1 + 40βθ + βθ^2)
θ = 50°C

Now we can solve this equation for θ.

First, let's simplify the equation by substituting the value of α:
Pθ = P0(1 + 40βθ + βθ^2)
Pθ = P0(1 + αθ + βθ^2)

Next, substitute θ = 50°C:
Pθ = P0(1 + α(50) + β(50)^2)

Now we have an equation with only Pθ, P0, α, β, and constants. We need the specific values of P0, α, and β to solve the equation further. Once we have those values, we can calculate Pθ.

Please provide the specific values of P0, α, and β so that we can continue the calculation and determine the temperature on the water vapor scale.