Advertisements
Advertisements
प्रश्न
A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10–1 °C–1.
उत्तर
Given: At 0oC, volume of glass vessel, Vg = 10 × 10 × 10 = 1000 cc = volume of mercury, VHg
Let the volume of mercury at 10°C be V'Hg and that of glass be V'g.
At 10oC, the additional volume of mercury than glass, due to heating, V'Hg – V'g = 1.6 cm3
So change in temperature, ΔT = 10°C
Coefficient of linear expansion of glass, αg = 6.5 × 10–6 °C–1
Therefore, the coefficient of volume expansion of glass, γg = 3 × 6.5 × 10–6°C–1
Let the coefficient of volume expansion of mercury be γHg.
We know that
V'Hg = VHg (1 + γHg ΔT) ...(1)
V'g = Vg (1 + γg ΔT) ...(2)
Subtracting (2) from (1) we get,
V'Hg – V'g = VHg – Vg + VHg γHg ΔT – Vg γg ΔT (as VHg = Vg)
\[\Rightarrow 1 . 6 = 1000 \times \gamma_{Hg} \times 10 - 1000 \times 6 . 5 \times 3 \times {10}^{- 6} \times 10\]
\[ \Rightarrow \gamma_{Hg} = \frac{1 . 6 + 19 . 5 \times {10}^{- 2}}{10000}\]
\[ \Rightarrow \gamma_{Hg} = \frac{1 . 6 + 0 . 195}{10000}\]
\[ \Rightarrow \gamma_{Hg} = \frac{1 . 795}{10000}\]
\[ \Rightarrow \gamma_{Hg} = 1 . 795 \times {10}^{- 4} \]
⇒ γHg ≅ 1.8 × 10-4°C-1
Therefore, the coefficient of volume expansion of mercury is 1.8× 10–4 °C–1.
APPEARS IN
संबंधित प्रश्न
The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:
R = Ro [1 + α (T – To)]
The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?
Answer the following:
The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
The pressures of the gas in a constant volume gas thermometer are 80 cm, 90 cm and 100 cm of mercury at the ice point, the steam point and in a heated wax bath, respectively. Find the temperature of the wax bath.
In a Callender's compensated constant pressure air thermometer, the volume of the bulb is 1800 cc. When the bulb is kept immersed in a vessel, 200 cc of mercury has to be poured out. Calculate the temperature of the vessel.
A piece of iron of mass 100 g is kept inside a furnace for a long time and then put in a calorimeter of water equivalent 10 g containing 240 g of water at 20°C. The mixture attains and equilibrium temperature of 60°C. Find the temperature of the furnace. Specific heat capacity of iron = 470 J kg−1 °C−1.
A platinum resistance thermometer reads 0° when its resistance is 80 Ω and 100° when its resistance is 90 Ω.
Find the temperature at the platinum scale at which the resistance is 86 Ω.
The temperatures of equal masses of three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C, and when B and C are mixed, it is 23°C. What will be the temperature when A and C are mixed?
Two metre scales, one of steel and the other of aluminium, agree at 20°C. Calculate the ratio aluminium-centimetre/steel-centimetre at (a) 0°C, (b) 40°C and (c) 100°C. α for steel = 1.1 × 10–5 °C–1 and for aluminium = 2.3 × 10–5°C–1.
A metre scale is made up of steel and measures correct length at 16°C. What will be the percentage error if this scale is used (a) on a summer day when the temperature is 46°C and (b) on a winter day when the temperature is 6°C? Coefficient of linear expansion of steel = 11 × 10–6 °C–1.
A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10–6 °C–1.
An aluminium can of cylindrical shape contains 500 cm3 of water. The area of the inner cross section of the can is 125 cm2. All measurements refer to 10°C.
Find the rise in the water level if the temperature increases to 80°C. The coefficient of linear expansion of aluminium is 23 × 10–6 °C–1 and the average coefficient of the volume expansion of water is 3.2 × 10–4 °C–1.
A cube of iron (density = 8000 kg m−3, specific heat capacity = 470 J kg−1 K−1) is heated to a high temperature and is placed on a large block of ice at 0°C. The cube melts the ice below it, displaces the water and sinks. In the final equilibrium position, its upper surface just goes inside the ice. Calculate the initial temperature of the cube. Neglect any loss of heat outside the ice and the cube. The density of ice = 900 kg m−3 and the latent heat of fusion of ice = 3.36 × 105 J kg−1.
A copper cube of mass 200 g slides down on a rough inclined plane of inclination 37° at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Specific heat capacity of copper = 420 J kg−1 K−1.
A circular disc made of iron is rotated about its axis at a constant velocity ω. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20°C to 50°C, keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2 × 10–5 °C–1.
Solve the following problem.
In a random temperature scale X, water boils at 200 °X and freezes at 20 °X. Find the boiling point of a liquid in this scale if it boils at 62 °C.
At what temperature, the reading of a fahrenheit thermometer will be three times that of celsius thermometer?
If the temperature on the Fahrenheit scale is 140 °F, then the same temperature on the Kelvin scale will be:
