Question

A gas mixture consists of $2$ moles of oxygen and $4$ moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

• A. $4\, RT$
• B. $9\, RT$
• C. $11\, RT$
• D. $15\, RT$

Answer 1

The Correct Option is C

For two moles of diatomic oxygen with no vibrational mode. 
\(U_{1} = 2\times \frac{5}{2} RT = 5RT\) 
For four moles of monoatomic Argon, 
\(U_{2} = 4\times \frac{3}{2} RT = 6RT\)
\(\therefore\quad U=U_{1}+ U_{2} = 5RT+6RT=11RT\)

Read more from the chapter: Internal Energy: Definition, Formula & Components

Answer 2

The Correct Answer is (C)

Real Life Applications

• Total internal energy can be used to understand the behavior of gas in different conditions.
• In chemical engineering, it can be used to know the efficiency and enthalpy of the reaction. 
• The luminosity of the star can be calculated using thermal energy in astrophysics. 

Question can also be asked as

• What is the total internal energy of a gas mixture consisting of 2 moles of oxygen and 4 moles of argon at temperature t? 
• How does the total internal energy of a gas mixture depend on the number of moles of oxygen and argon? 
• What is the effect of neglecting the vibrational modes on the total internal energy of a gas mixture? 
• What is total internal energy and its significance? 

Answer 3

The Correct Answer is (C)

The inherent form of energy that is present in the system is called internal energy, due to motion. The total internal energy can be calculated by adding the total kinetic energy, potential energy, and electric energy of the atoms. The properties of internal energy are as follows: 

• The symbol U is used to denote the internal energy.
• Joules (J) is the unit of measurement for internal energy.
• It is an extensive quantity.
• It is present in various forms of energy.

The internal energy of a closed system

The formula for internal energy is ΔU = q + W, 

Here, U is the change in internal energy 

q denotes heat 

W is the mechanical work 

Components of Internal energy 

The component of the internal energy in a system are: 

• Thermal energy
• Chemical energy
• Nuclear energy

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Related concepts
Chemical energy	Heat transfer	Latent heat
Work done	Heat	Thermodynamics processes