8) (10 points) Write a triple integral and use it to find the volume of the tetrahedron bounded by x+2y+z = 2, x = 2y, x=0, and z=0. 9) (15 points) The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p is the pressure, V is the volume, and T is the temperature. For an ideal gas, PV = nRT where the number of moles n and R (gas-specific) are constants. a) (3 points) Write the differential form dU for the internal energy. b) (5 points) Assuming the volume V is held constant, find an expression for the . a heat capacity c, where , = (agjv c) (5 points) Assuming the volume V is held constant, find (gg)v d) (2 points) For an ideal gas, please provide physical interpretations of au au Cp = (a_p)" and (E)v