Near the surface of Venus, its atmosphere has a pressure fv = 91 times the pressure of Earth's atmosphere, and a particle density of around rhov = 1.05 * 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? g

We shall use gas law equation and modify it to include number density of particle as follows

PV = n RT, n is no of moles

P = (n / V) RT

At earth, P = a atm, n = 6.02 x 10²⁶/22.4, V = 1 m³, R is constant, T = 273

(1 mole of a gas occupies 22.4 litre volume and contains 6.02 x 10²³ no of gas molecules. 1 liter = 10⁻³ m³.)

1 = 6.02 x 10²⁶ x R x 273 / 22.4

At Venus P = 91 atom, n = 1.05 x 10²⁷, V = 1 m³, R is constant, T = ?

91 = 1.05 x 10²⁷ R x T

dividing the two equations

91 / 22.4 = 1.05 x 10²⁷ R x T / 6.02 x 10²⁶ x R x 273

91 x 6.02 x 273 / 22.4 = 1.05 x 10 T

T = 91 x 6.02 x 273 / (10.5 x 22.4)

= 635.86 K

= 362.86 degree Celsius.