Two cylienders fitted with pistons and placed as shown, connected with string through a small tube of negligible volume, are filled with gas at pressure `P_(0)` and temperature `T_(0)`. The radius of smaller cylinder is half of the other. If the temperature is increased to `2 T_(0)`, find the pressure if the piston of bigger cylinder moves towards left by 1 metre ?

Options

A. `(4)/(5) P_(0)`
B. `(3)/(5) P_(0)`
C. `(2)/(5) P_(0)`
D. `(5)/(4) P_(0)`

Answer

D

Explanation

d. Initial volume `= 1 xx [pi R^(2) + (pi R^(2))/(4)] = (5)/(4) pi R^(2)`
Piston moves towards left by `1 m` on heating. Additional volume available due to heating is
`1 xx pi R^(2) - (1 xx pi R^(2))/(4) = (3)/(4) pi R^(2)`
Total volume after heating `= 2 pi R^(2)`
`P_(0) xx (5)/(4) pi R^(2) = nRT_(0)`
After heating, `P_(2) xx 2 pi R^(2) = nR xx 2 T_(0)`
`((P_(1))/(P_(2))) xx (5)/(4) xx (1)/(2) = (1)/(2)`
`P_(2) = 5 P_(0)//4`