What is the average surface temperature of Uranus

Answer:

To determine the relationship between pressure and temperature in this scenario, we can use the ideal gas law.

The ideal gas law states that PV = nRT, where P represents pressure, V represents volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents temperature in Kelvin.

Since we only have the initial and final pressures and temperatures, we can compare them using the ideal gas law equation by setting up the following ratio:

(P₁T₁) / (P₂T₂) = (V₁n₁R) / (V₂n₂R)

Since the volume, number of moles, and gas constant remain constant, we can simplify the equation:

(P₁T₁) / (P₂T₂) = 1

Now, we can substitute the given values into the equation:

(53.0 atm * T₁) / (35.2 atm * 12.0°C) = 1

To solve for T₁, we need to convert 12.0°C to Kelvin by adding 273.15:

(53.0 atm * T₁) / (35.2 atm * (12.0 + 273.15) K) = 1

Simplifying the equation further:

(53.0 atm * T₁) / (35.2 atm * 285.15 K) = 1

Now, we can solve for T₁:

(53.0 atm * T₁) = (35.2 atm) * (285.15 K)

Dividing both sides of the equation by 53.0 atm:

T₁ = (35.2 atm * 285.15 K) / 53.0 atm

Calculating the numerical value:

T₁ ≈ 189.5 K

Therefore, when the pressure changes from 53.0 atm to 35.2 atm, the temperature changes from approximately 12.0°C to 189.5 K.