8. The ideal gas law PV volume, and temperature of a confined gas, where n is the number of moles of R is the universal gas constant. Show that (@V/&T)(@T/ƏP)(@P/ƏV) = -1. nRT is used to describe the relationship between pressure, gas and

A force, F(x) object? 100x, is applied to an object to move it from x = 3 to x = 5. How much work was applied to the 50 800 100 200 The average value of f(x) = In 3x on [2,5] is approximately 2.32. true false The distance a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t) = = -24 (in feet/sec) is: ○ 54 ft 1866 ft 12 ft 16 ft If a particle is traveling according to the velocity equation v(t) = 2+3 +5 (in m/s), then its displacement over its first 2 seconds of travel is equal to 18 m. true false

A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.15 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.03 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass= kg

(i) Using the integral definition below, find the average density of the Earth given the following information: Oceanic Plate where can be written as 3-5 miles thick ● Diagram not drawn to scale 1400 miles Thick 1800 miles thick 5-25 miles thick 800 miles thick Continental Plate Mantle (Flows with the consistancy of asphalt) Scale everything in terms of the radius of the Earth R ( 4000 miles here for simplicity), so that in terms of the variable y r/R, 0 ≤ y ≤ 1, the integral for the average density p=2³3r²p(r)dr Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state} p=3√ 1²p(v)dy, p(y) = P₁, 0≤ y ≤yi, = P2, y1 ≤y ≤y2, = P3, y2 ≤y ≤ y3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ yı): Earth's inner core has the highest density p₁ 13 g/cm³. OUTER CORE (1 ≤ y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤ y ≤y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick.