An ideal gas at `NTP` is enclosed in an adiabatic vertical cylinder havin an area of cross section `A=27 cm^(2)` between two light movable pistons as shown in figure. Spring with force constant `K=37-- N//m` is in a relaxed state initially. Now the lower position is moved upwards a distance `h//2`, `h` being the initial length of gas column . It is observed that the upper piston moves up by a distance `h//16`. Final temperature of gas` 4//3 xx 273 K`. Take `gamma` for the gas to be `3//2`.

When the lower pistone is moved upwards a distance `h//2`, the compression.

Options

A. leads to cooling
B. takes place isothermally
C. takes place adiabatically
D. leads to heating

Answer

C, D

Explanation

First adiabatic compression takes place
`gamma = 1.5`
`V_(0)=Ah, V_(1)=(Ah)/( 2)`
`T_(0)V_(0)^(gamma-1)implies T_(1)=sqrt(2)T_(0)gt T_(0)`