A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L1 and L2 are the lengths of the gas column before and after expansion respectively, then T1/T2 is given by
(L1/L2) ^(2/3)
L1/L2
L2/L1
(L2/L1) ^(2/3)
As we discussed in concept
Equation of state -
- wherein
On solving
For adiabatic process:
Option 1)
(L1/L2) ^(2/3)
This option is incorrect.
Option 2)
L1/L2
This option is incorrect.
Option 3)
L2/L1
This option is incorrect.
Option 4)
(L2/L1) ^(2/3)
This option is correct.