Mixture Of Gases And Internal Energy

Question

A rigid insulated tank contains a mixture of 2 moles of a monatomic gas and 2 moles of a diatomic gas at temperature T, so what is the total internal energy of the mixture?

RankGuru · Accepted Answer

Computing the mixture's energy applies the internal energy expressions from NCERT Class 11, Chapter 13 (Kinetic Theory), which give the internal energy of $n$ moles as $U = \frac{f}{2}nRT$, where $f$ is the number of degrees of freedom. For the monatomic component with $f = 3$, the energy is $U_1 = \frac{3}{2}	imes 2 	imes RT = 3RT$. For the diatomic component with $f = 5$ at room temperature, the energy is $U_2 = \frac{5}{2}	imes 2 	imes RT = 5RT$. Since internal energy is additive, the total is $U = U_1 + U_2 = 3RT + 5RT = 8RT$. The option 5RT counts only the diatomic contribution. The option 10RT wrongly treats both gases as diatomic. The option 6RT wrongly treats both as monatomic. The additivity works because internal energy is an extensive property, so the energies of independent components in thermal equilibrium at the same temperature simply add together. A plausibility check confirms the total: the diatomic gas, having more degrees of freedom, must store more energy than the monatomic gas at the same temperature and mole number, and indeed $5RT > 3RT$, with their sum $8RT$ lying sensibly between the all-monatomic value $6RT$ and the all-diatomic value $10RT$.

Mixture Of Gases And Internal Energy

Select the correct option:

🔒 Solution Hidden from View

More kinetic theory of gases Practice Questions

How does the mean free path of molecules in a gas sample change if the number density of molecules i...

In a laboratory vacuum chamber the pressure of a gas is reduced to one-tenth of its initial value wh...

A weather balloon contains 2 moles of an ideal gas, so approximately how many gas molecules are pres...

Equal volumes of two different ideal gases are compared at the same temperature and pressure, so wha...

As the temperature of a gas sample is increased, how does the shape of its Maxwell molecular speed d...

Which of the following assumptions is fundamental to the kinetic theory model of an ideal gas as des...

Two containers hold helium and oxygen respectively at the same absolute temperature, so how do the a...

When the absolute temperature of a fixed sample of ideal gas is raised from 300 K to 600 K, by what ...

Consider a tank of nitrogen molecules each of molar mass 28 grams per mole maintained at 300 K, so w...

Hydrogen and oxygen samples are kept at the same temperature, and given that oxygen is sixteen times...

For a sample of ideal gas at a given temperature, arrange the most probable speed, the average speed...

A rigid diatomic gas molecule at ordinary room temperature, ignoring vibrational modes, possesses ho...

About This Question

Solution