Rising Column Creates Problem

There is wet wood burning in a fire place on the ground. Seven meters above ground, the smoke is at a temperature of $t_7=40'C$ . Disregard the exchange of heat with the surrounding air and assume that the the atmospheric pressure at the ground is constant in time and equal to $p_0=1000hPa$ ; the air temperature $t_0=20'C$ is independent of height.Assume that the smoke represents an ideal gas of a molar mass $\mu=29g/mol$ (i.e equal to the molar mass of the air),and of a molar specific heat at constant volume $C_v=2.5R$ ; .How high will the smoke column rise.

Express your answer in $m$ .

Take $R=8.31J/kg.K$