Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
(a) Let the correct length measured by a metre scale made up of steel 16 °C be L.
Initial temperature, t1 = 16 °C
Temperature on a hot summer day, t2 = 46 °C
So, change in temperature, Δθ = t2
\[-\]t1 = 30 °C
Coefficient of linear expansion of steel,
\[\alpha\]= 1.1 × 10–5 °C-1
Therefore, change in length,
ΔL = L αΔθ = L × 1.1 × 10–5 × 30
% of error =`((ΔL)/L × 100) %`
= `((L∝Δθ)/L × 100)%`
=[1.1 × 10-5 × 30 ×100]%
=3.3 × 10-2 %
(b) Temperature on a winter day, t2 = 6 °C
So, change in temperature, Δθ = t1
\[-\]t2 = 10 °C
ΔL = L2
\[-\] L1 = L αΔθ = L × 1.1 × 10–5 × 10
`text/"% of error" = (ΔL/L × 100)%`
\[ = \left( \frac{L\alpha \Delta\theta}{L} \times 100 \right) % \]
\[ = 1 . 1 \times {10}^{- 5} \times 10 \times 100 % \]
\[ = 1 . 1 \times {10}^{- 2} \]
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?
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)?
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.
In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature T. How can we verify whether this is true or not? Do we have to apply the kinetic theory of gases? Do we have to depend on experimental result that the pressure is proportional to temperature?
Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.
The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature on a centigrade mercury scale when this thermometer reads 32°?
Which of the following pairs represent units of the same physical quantity?
A constant-volume thermometer registers a pressure of 1.500 × 104 Pa at the triple point of water and a pressure of 2.050 × 104 Pa at the normal boiling point. What is the temperature at the normal boiling point?
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)?
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.
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.
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.
A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will the rod exert on one of the clamps? Area of cross-section of the rod is 2.00 mm2. Coefficient of linear expansion of steel is 12.0 × 10–6 °C–1 and Young's modulus of steel is 2.00 × 1011 Nm–2.
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.
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 |
A torsional pendulum consists of a solid disc connected to a thin wire (α = 2.4 × 10–5°C–1) at its centre. Find the percentage change in the time period between peak winter (5°C) and peak summer (45°C).
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.
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.
If the temperature on the Fahrenheit scale is 140 °F, then the same temperature on the Kelvin scale will be:
Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.
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 ______.
Convert 37 °C (normal body temperature) to Kelvin.
Which of the following correctly describes an adiabatic wall?
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?
Which of the following is NOT a characteristic of a good thermometer?
