In a constant-volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a U-tube connected to the gas at one end. When the bulb is placed at room temperature $27.0^\circ\text{C}$, the mercury column in the arm open to the atmosphere stands $5.00\,\text{cm}$ above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes $45.0\,\text{cm}$. Calculate the temperature of the liquid (atmospheric pressure $= 75.0\,\text{cm}$ of mercury).