A cylinder whose inside diameter is `4.00 cm` contains air compressed by a piston of mass `m = 13.0 kg` which can slide freely in the cylinder. The entire arrangement is immersed in a water bath temperature can be controlled. The system is initially in equilibrium at temperature `t_i = 20^@ C`. The initial height of the piston above the bottom of the cylinder is `h_i = 4.00 cm`. The temperature of the water bath is gradually increased to afinal temperature `t_f = 100^@ C`. Calculate the final height `h_f` of the piston.
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Answer

C

Explanation

`p = constant`
`:. V prop T`
or `h prop T`
`:. (h_f)/(T_f) = (h_i)/(T_i) h_i`
or `h_(f) = ((T_(f))/(T_(i))) h_(i)`
= `((273 + 100)/(273 + 20)) (4) = 5.09 cm`.