Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
At 20°C, length of the metre scale made up of steel, Lst= length of the metre scale made up of aluminium, Lal
Coefficient of linear expansion for aluminium, αal = 2.3 × 10–5 °C-1
Coefficient of linear expansion for steel, αst = 1.1 × 10–5 °C-1
Let the length of the aluminium scale at 0°C, 40°C and 100°C be L0al, L40al and L100al.
And let the length of the steel scale at 0°C, 40°C and 100°C be L0st, L40st and L100st.
(a) So, L0st(1 – αst × 20) = L0al(1 – αal × 20)
\[\frac{L_{0st}}{L_{0al}} = \frac{\left( 1 - \alpha_{al} \times 20 \right)}{\left( 1 - \alpha_{st} \times 20 \right)}\]
\[ \Rightarrow \frac{L_{0st}}{L_{0al}} = \frac{1 - 2 . 3 \times {{10}^-}^5 \times 20}{1 - 1 . 1 \times {10}^{- 5} \times 20}\]
\[ \Rightarrow \frac{L_{0st}}{L_{0al}} = \frac{0 . 99954}{0 . 99978}\]
\[ \Rightarrow \frac{L_{0st}}{L_{0al}} = 0 . 999759\]
(b) \[\frac{L_{40 al}}{L_{40 st}} = \frac{L_{0 al} \left( 1 + \alpha {}_{al} \times 40 \right)}{L_{0 st} \left( 1 + \alpha_{st} \times 40 \right)}\]
\[ \Rightarrow \frac{L_{40 al}}{L_{40 st}} = \frac{L_{0 al}}{L_{0 st}} \times \frac{\left( 1 + 2 . 3 \times {10}^{- 5} \times 40 \right)}{\left( 1 + 1 . 1 \times {10}^{- 5} \times 40 \right)}\]
\[ \Rightarrow \frac{L_{40 al}}{L_{40 st}} = \frac{0 . 99977 \times 1 . 00092}{1 . 00044}\]
\[ \Rightarrow \frac{L_{40 al}}{L_{40 st}} = 1 . 0002496\]
(c) \[\frac{L_{100 al}}{L_{100 st}} = \frac{L_{0 al} \left( 1 + \alpha {}_{al} \times 100 \right)}{L_{0 st} \left( 1 + \alpha_{st} \times 100 \right)}\]
\[ \Rightarrow \frac{L_{100 al}}{L_{100 st}} = \frac{0 . 99977 \times 1 . 0023}{1 . 0023}\]
\[ \Rightarrow \frac{L_{100 al}}{L_{100 st}} = 1 . 00096\]
APPEARS IN
संबंधित प्रश्न
The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.
Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?
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)?
Two ideal gas thermometers Aand Buse oxygen and hydrogen respectively. The following observations are made:
| Temperature | Pressure thermometer A | Pressure thermometer B |
| Triple-point of water | 1.250 × 105 Pa | 0.200 × 105 Pa |
| Normal melting point of sulphur | 1.797 × 105 Pa | 0.287 × 105 Pa |
(a) What is the absolute temperature of the normal melting point of sulphur as read by thermometers Aand B?
(b) What do you think is the reason behind the slight difference in answers of thermometers Aand B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?
A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of –39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm? Co-efficient of linear expansion of brass = 2.0 × 10–5 K–1; Young’s modulus of brass = 0.91 × 1011 Pa.
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
In which of the following pairs of temperature scales, the size of a degree is identical?
(a) Mercury scale and ideal gas scale
(b) Celsius scale and mercury scale
(c) Celsius scale and ideal gas scale
(d) Ideal gas scale and absolute scale
Which of the following pairs represent units of the same physical quantity?
The pressure measured by a constant volume gas thermometer is 40 kPa at the triple point of water. What will be the pressure measured at the boiling point of water (100°C)?
The pressure of the gas in a constant volume gas thermometer is 70 kPa at the ice point. Find the pressure at the steam point.
An aluminium vessel of mass 0.5 kg contains 0.2 kg of water at 20°C. A block of iron of mass 0.2 kg at 100°C is gently put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminium, iron and water are 910 J kg−1 K−1, 470 J kg−1 K−1 and 4200 J kg−1 K−1 respectively.
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.
Four 2 cm × 2 cm × 2 cm cubes of ice are taken out from a refrigerator and are put in 200 ml of a drink at 10°C. (a) Find the temperature of the drink when thermal equilibrium is attained in it. (b) If the ice cubes do not melt completely, find the amount melted. Assume that no heat is lost to the outside of the drink and that the container has negligible heat capacity. Density of ice = 900 kg m−3, density of the drink = 1000 kg m−3, specific heat capacity of the drink = 4200 J kg−1 K−1, latent heat of fusion of ice = 3.4 × 105 J kg−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 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.
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.
Two steel rods and an aluminium rod of equal length l0 and equal cross-section are joined rigidly at their ends, as shown in the figure below. All the rods are in a state of zero tension at 0°C. Find the length of the system when the temperature is raised to θ. Coefficient of linear expansion of aluminium and steel are αa and αs, respectively. Young's modulus of aluminium is Ya and of steel is Ys.
| Steel |
| Aluminium |
| Steel |
Answer the following question.
How a thermometer is calibrated?
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.
The graph between two temperature scales A and B is shown in figure. Between upper fixed point and lower fixed point there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by ______.
Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.
The Zeroth Law of Thermodynamics is the basis for which of the following?
At what temperature do the Celsius and Fahrenheit scales show the same reading?
Which thermometer is considered the most accurate?
A wall that allows free exchange of heat between two systems is called ______.
Which of the following correctly describes an adiabatic wall?
A mercury thermometer is placed under a patient's tongue. Which sequence correctly describes what happens before a reading is taken?
A platinum wire is used as the thermometric substance in a resistance thermometer. What is the thermometric property being utilised here?
A mercury thermometer has a column length of 20 mm at the ice point and 170 mm at the steam point. If the column length is 65 mm, what is the temperature?
