An insulated cylinderical vessel filled with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel . The cylinder contains a gas at `0^@C`.When the gas is heated to `100^@C`, the piston moves through a length of 5 cm . Length of the cylindrical vessel in cm is

Options

A. 15.65cm
B. 27.3cm
C. 38.6cm
D. 64.6cm

Answer

D

Explanation

According to charls' law, `V_(1)/V_(2) =T_(1)/T_(2)`
`l_(1)/l_(2) = T_(1)/T_(2)` [`because` Volume is proportional to length]
`(l+5)/(l-5) =(273+100)/(273-0)`
273 l + 1365 = 373l -1865
`therefore l= 3230/100 = 32.3`
Length of cylinder, 2l=64.6cm