Question

Heat capacity and degrees of freedom A sealed container holds 5 moles of a diatomic gas.
A. Calculate the heat capacity of one molecule of this gas, and then the heat capacity of the whole sample, assuming all quadratic degrees of freedom are available.
B. Suppose the gas is oxygen (with molar mass 32 ! "#$). Use your result above to compute the specific heat of oxygen.
C. Look up the empirically measured specific heat of O2 gas at 300 K and compare with your answer. Are we correct in assuming all the degrees of freedom are available

Answer 1

Answer:

Explanation:

From the concept of equipartition energy, the energy for the respective degree of freedom is $\dfrac{1}{2}K_BT$and for diatomic gas, the degree of freedom = 7

Thus, the heat capacity per molecule can be represented as:

$C_v = \dfrac{7}{2} K_B$

For a heat capacity holding 5 moles of gas; we have:

= $5\times \dfrac{7}{2}\times R$

Therefore;

C = $5\times \dfrac{7}{2}\times 8.314$

C = 145.5

B.

The specific heat capacity = C/mass

where the mass of 5 moles of oxygen gas = 32 × 5 g

= 160 g

Thus; specific heat = 145.5/160

specific heat = 0.91 J/gK or 910 J/kg/K

C)

From the tables of specific heat at the given temperature of 300 K, we have:

0.918 J/gk and the estimated value is 0.92 J/gk

Therefore, the results are very near when compared to one another.

Answer 2

The branch of science in deals with chemicals and bonds is called chemistry. The reaction which requires heat to complete the reaction is called an endothermic reaction.

The correct answer to the question is option C has he empirically measured the specific heat of O2 gas at 300 K and compared it with your answer. Are we correct in assuming all the degrees of freedom are available?

Heat capacity?

• Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature.
• The SI unit of heat capacity is joule per kelvin. Heat capacity is an extensive property.

The heat capacity is as follows:-

$C_v =\frac{7}{2}Kb \\\\=5*\frac{7}{2} *R\\\\=5*\frac{7}{2}*8.314\\\\C= 145.5$

The specific heat capacity = C/mass, where the mass of 5 moles of oxygen gas = 32 × 5 g

= 160 g

Thus; specific heat = 145.5/160

specific heat = 0.91 J/gK or 910 J/kg/K.

Hence, the correct answer to the question is option C.

For more information about the question, refer to the link:-

https://brainly.com/question/1453843