Answer:

The internal energy of two moles of oxygen at 400 K is 12035 J.

Explanation:

To find the internal energy of two moles of oxygen at 400 K, we can use the concept of molar specific heat capacity. The molar specific heat capacity of a substance is the amount of heat required to raise the temperature of one mole of that substance by 1 Kelvin (or 1 degree Celsius).

Given:

Internal energy of one mole of oxygen at 300 K (U1) = 6235 J

Temperature of two moles of oxygen (T2) = 400 K

Now, let's calculate the internal energy of two moles of oxygen (U2) at 400 K:

Using the formula for molar specific heat capacity (C):

Q = n * C * ΔT

where:

Q is the heat energy,

n is the number of moles,

C is the molar specific heat capacity, and

ΔT is the change in temperature.

Since Q = U2 - U1, where U2 is the internal energy of two moles of oxygen at 400 K and U1 is the internal energy of one mole of oxygen at 300 K, we can rearrange the formula to solve for U2:

U2 = U1 + n * C * ΔT

Since we are dealing with two moles of oxygen, n = 2.

Now, we need the molar specific heat capacity of oxygen, which is approximately 29 J/(mol*K).

ΔT = T2 - T1 = 400 K - 300 K = 100 K

Now, we can calculate the internal energy of two moles of oxygen at 400 K:

U2 = 6235 J + 2 mol * 29 J/(mol*K) * 100 K

U2 = 6235 J + 5800 J

U2 = 12035 J

So, the internal energy of two moles of oxygen at 400 K is 12035 J.