Answer:
a) the increase in internal energy is 3211.78 J
b) dU = 3854.14 J
c) dU[tex]_{T}[/tex] = 1927.06 J
Explanation:
Given the data in question;
Foe a diatomic gas, the degree of freedom are as follow;
lets consider the positional degree of freedom
transitional df = 3
rotational df = 2
vibrational ff = 1
now, the internal energy given by;
U = Nf × 1/2NKT = Nf×1/2×nRT
where Nf is the number of degree of freedom
N is Number of atoms or molecules
n = number of molecules
L is Boltzmann constant
R is universal gas constant
so change in internal energy , change in T is given by
dU = Nf × 1/2 × nT dT
n = 2.37 moles
dT = 65.2 K
R = 8.314 J/mol.J
a)
Find the increase in internal energy if only translational and rotational motions are possible
since rotational and transitional motion are involved ;
Nf = 3(trasitional) + 2(rotational) = 5
so,
dU = 5 × 1/2 × nRdT
we substitute
dU = 5 × 0.5 × 2.37 × 8.314 × 65.2
dU = 3211.78 J
Therefore, the increase in internal energy is 3211.78 J
b)
Find the increase in internal energy if translational, rotational, and vibrational motions are possible.
Nf = 3 + 2 + 1 = 6
dU = 6 × 1/2 × nRdT
dU = 6 × 0.5 × 2.37 × 8.314× 65.2
dU = 3854.14 J
c)
How much of the energy calculated in (a) and (b) is translational kinetic energy?
dU[tex]_{T}[/tex] = 3 × 0.5 × 2.37 × 8.314 × 65.2
dU[tex]_{T}[/tex] = 1927.06 J
