Gce Model Questions Vol1 2024 Physics Question 4

A vertical glass tube of internal cross‑section \(A=1.0\times10^{-4}\ \text{m}^{2}\) is sealed at the bottom and open at the top. The tube is placed in a water reservoir so that the open end is at the water surface. Initially a column of air of length \(L_{0}=0.08\ \text{m}\) occupies the upper part of the tube; the remaining lower part (total tube length \(0.20\ \text{m}\)) is filled with water. The air is at temperature \(T_{0}=293\ \text{K}\) and pressure equal to atmospheric pressure \(P_{\text{atm}}=1.01\times10^{5}\ \text{Pa}\). The water column therefore exerts an additional hydrostatic pressure \(\rho g h_{0}\) on the air, where \(\rho=1000\ \text{kg\,m}^{-3}\) and \(g=9.8\ \text{m\,s}^{-2}\). The air is heated uniformly to \(T_{1}=353\ \text{K}\) while the tube remains open to the reservoir (the water can move freely). Assuming the water temperature stays at \(293\ \text{K}\), determine the new length \(L_{1}\) of the air column after heating.