Question
Download Solution PDFWhich of the following best represents the relationship between internal energy 'U' of an ideal gas and its absolute temperature 'T'?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 2)
CONCEPT:
- Ideal gas: An ideal gas is a hypothetical concept where it is assumed that:
- There are no intermolecular forces of attraction between the molecules of the gas.
- The volume occupied by the gas molecules is negligible.
- The kinetic energy of ideal gas:
- The kinetic energy of the gas comes from the temperature of the gas. Greater the temperature, the more the kinetic energy.
The average kinetic energy per molecule of a gas is given by:
Where T is the temperature of the gas IN Kelvin and kB is the Boltzmann's constant (1.38 × 10-23 J/K)
EXPLANATION:
- There are no attractive forces between the gas molecules of an ideal gas. Hence, the internal energy of the gas will only be kinetic energy i.e. U = KE.
The kinetic energy of an ideal gas is dependent on its temperature as:
⇒ KE ∝ T
⇒ U ∝ T
Therefore, the plot of internal energy vs time will be a straight line through the origin as shown in option 2).
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