4. Venus and the Earth are very similar in mass/size as planets, but their atmospheres are quite different. The surface pressure on Earth is Po= 101.325 kPa and the average mass density of the atmosphere is 1.22 kgm-3. On Venus the surface pressure is 93 times higher than the Earth and the average mass density of the atmosphere at the surface is 55 times higher than the Earth. a. Assume that the atmosphere of both planets can be represented as a spherical shell of thickness h having a uniform density p. Derive an equation for h. b. Compute the value for h for Venus and the Earth. c. Now substitute the equation for the pressure P of an ideal gas of temperature T and density p into your answer from part a) and simplify. What is this value of h commonly called in describing a planetary atmosphere? d. In reality, the mass density of the atmosphere decreases with height. Assuming the temperature is constant, what is the actual atmospheric pressure at height h on Earth and Venus assuming hydrostatic equilibrium holds? Assume a constant temperature of 300K for Earth and 700K for Venus and assume pure CO2 for Venus' atmosphere and pure N2 for Earth's atmosphere. 4. Venus and the Earth are very similar in mass/size as planets, but their atmospheres are quite different. The surface pressure on Earth is Po= 101.325 kPa and the average mass density of the atmosphere is 1.22 kgm-3. On Venus the surface pressure is 93 times higher than the Earth and the average mass density of the atmosphere at the surface is 55 times higher than the Earth. a. Assume that the atmosphere of both planets can be represented as a spherical shell of thickness h having a uniform density p. Derive an equation for h. b. Compute the value for h for Venus and the Earth. c. Now substitute the equation for the pressure P of an ideal gas of temperature T and density p into your answer from part a) and simplify. What is this value of h commonly called in describing a planetary atmosphere? d. In reality, the mass density of the atmosphere decreases with height. Assuming the temperature is constant, what is the actual atmospheric pressure at height h on Earth and Venus assuming hydrostatic equilibrium holds? Assume a constant temperature of 300K for Earth and 700K for Venus and assume pure CO2 for Venus' atmosphere and pure N2 for Earth's atmosphere