In a constant volume gas thermometer, the pressure of the working gas is measured by the differenced 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 the room temperature `27.0^0 C`, the mercury column in the arm open to atmosphere stands `5.00 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 Cm`. Calculate the temperature of the liquid. (Atmospheric pressure `= 75.0cm` of mercury).

Explanation

The pressure of the gas = atmospheric pressure + the pressure due to the difference in mercury levels At `27^0 C`, the pressure is `75cm + 5cm = 80cm` of mercury. At the liquid temperature, the pressure is `75cm + 45cm = 120cm` of mercury. Using `T_2 = P_2/P_1 T_1`, the temperature of the liquid is
`T= 120/80 xx (27.0 + 273.15) K = 450.22K`.
`= 177.07^0 C = 177^0 C`.