Question

A cylindrical tank of height 2 m has its top closed by a tight fitting friction-less piston of negligible mass. The helium gas inside the cylinder is at a pressure of 1 atmosphere. The gas is compressed slowly by pouring mercury on the piston. If the temperature of the gas is maintained constant, then the mercury will spill over the top of the cylinder when the piston is at a height of

• A. 48 cm
• B. 76 cm
• C. 124 cm
• D. 152 cm

Answer 1

The correct option is B 76 cm

For Boyle's law to hold

$P_1{V}_1=P_2{V}_2$

$76\times A\times 200=(76+h)\times A\times (200-h)$

$76\times 200=(76+h)(200-h)$

$76\times 200=15200-76h+200h-h^2$

$h^2+124h-15200+15200=0$

$h^2=+124h$

$h=+124㎝$

Hence, height of piston$=200-124$

$=76㎝$