Dry hydrogen is trapped by pellet of mercury in a uniform capillary tube closed at one end. If the length of the column of hydrogen at 27°C is 1.0m, at what...

The problem involves a trapped gas at a fixed volume in a closed-end tube, and we are asked to find the temperature at which the length of the gas column will increase to a specified value. This can be solved using the relationship between the volume of a gas and its temperature, known as Charles's Law. According to Charles's Law, the volume of a gas is directly proportional to its temperature at constant pressure. Mathematically, this can be expressed as: V1/T1 = V2/T2 where V1 and T1 are the initial volume and temperature, respectively, and V2 and T2 are the final volume and temperature, respectively. In this problem, the volume of the gas is constant since it is trapped by the mercury pellet, so we can simplify the equation to: T1/T2 = L1/L2 where L1 and L2 are the initial and final lengths of the gas column, respectively. We are given that the initial length of the gas column is 1.0 m at a temperature of 27°C (which can be converted to 300.15 K). We are asked to find the temperature at which the length of the gas column will increase to 1.20 m. Using the above equation, we can solve for T2: T2 = (L2/L1) x T1 T2 = (1.20 m / 1.0 m) x 300.15 K T2 = 360.18 K We can convert this temperature to degrees Celsius by subtracting 273.15: T2 = 87.03°C Therefore, the correct option is (d) 87.0°C.