What is the internal energy of 4.00 mol of diatomic nitrogen gas, N2, at 455 K? Please show work & thank you in advance!

The internal energy of an ideal gas is given by:

where
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
k=3 for monoatomic gases, k=5 for diatomic gases

In this problem, we have n=3.0 mol of a diatomic gas (k=5) at T=288 K. Substituting these numbers into the equation, we find the internal energy of the gas:

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.