A) \[q=0,\text{ }\Delta T<0\] and \[w>0\]
B) \[q<0,\text{ }\Delta T=0\] and \[w=0\]
C) \[q>0,\text{ }\Delta T>0\] and \[w>0\]
D) \[q=0,\text{ }\Delta T=0\] and \[w=0\]
Correct Answer: D
Solution :
| [d] Free expansion \[\Rightarrow \text{ }{{P}_{ex}}=0\] |
| \[\therefore w=-{{P}_{ex}}\Delta V=0\] |
| \[\because \] Adiabatic process \[\Rightarrow q=0\] |
| also, \[\Delta U=q+w\] [ first law of thermodynamics] |
| \[\therefore \Delta U=0\] |
| \[\because \] Internal energy of an ideal gas is a function of temperature |
| \[\therefore \] If internal energy remains constant |
| \[\therefore \Delta T=0\] |
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