Identify the characteristics of an adiabatic process in a monoatomic gas.
Text Solution
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In an adiabatic process, the key characteristics for a monoatomic gas are:
No Heat Exchange: The adiabatic process occurs without heat transfer, meaning
.
Work Done and Internal Energy Change: The work done on or by the system is equal to the change in internal energy. Mathematically, this is expressed as:

Substituting the given values for atmospheric pressure
(1 atm) and volume
:

where
is the change in internal energy and
is the work done.
Work and Temperature Relationship: The work done when changing the temperature from
to
is proportional to the difference between these temperatures. This relationship can be expressed as:
Work Done
Here,
is the number of moles,
is the molar heat capacity at constant volume, and
is the change in temperature.
From these characteristics, the correct features of an adiabatic process in a monoatomic gas relate to the relationships involving work done and temperature change, specifically options and (E).
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