Question

Calculate the internal energy of one mole of helium
gas at a temperature of 280K. Assume ideal gas behavior.

Answer 1

U = n*c_v*T

c_v = R/(k - 1)

k is the adiabatic index, k=5/3 for Helium, because it is monatomic

U = n*R*T/(k - 1)

U = 1*8.314*280/(2/3)

U = 3491.88 J

Answer 2

Formula:
U = n*c_v*T

n is number of moles
c_v is the molar isochoric specific heat capacity
T is temperature in Kelvin

Formula for c_v:
c_v = R/(k - 1)

R is the universal gas constant
k is the adiabatic index, k=5/3 for Helium, because it is monatomic

Thus:
U = n*R*T/(k - 1)

Data:
k:=5/3; R:=8.314 J/mole-K; n:= 1 mole; T:=280 K;
U= 1*8.314*280/(5/3-1)
Result:
U = 3491.88Joules