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A cylinder whose inside diameter is \( 4.00 \mathrm{~cm} \) contains air compressed by a piston of mass \( m=13.0 \mathrm{~kg} \) which can slide freely in the cylinder. The entire arrangement is immersed in a water bath whose temperature can be controlled. The system is initially in equilibrium at temperature \( t_{i}=20^{\circ} \mathrm{C} \). The initial height of the piston above the bottom of the cylinder is \( h_{i}=4.00 \mathrm{~cm} \). The temperature of the water bath is gradually increased to a final temperature \( t_{f}=100^{\circ} \mathrm{C} \). Calculate the final height \( h_{f} \) of the piston.
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