Advertisements
Advertisements
Question
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?
Advertisements
Solution 1
Here, R0 = 101.6 Ω; T0 = 273.16 K Case (i) R1= 165.5 Ω; T1 = 600.5 K, Case (ii) R2 = 123.4 , T2 = ?
Using the relation R = R0[1 + α (T – T0)]
Case (i) 165.5 = 101.6 [1 + α (600.5 – 273.16)]
`alpha= (165.5 - 101.6)/(101.6xx(600.5-273.16)) = 63.9/(101.6xx327xx37)`
Case II `123.4 = 101.6 [1 + alpha(T_2 - 273.16)]`
or `123.4 = 101.6 [1+ 63.9/(101.6xx327.34)(T_2-273.16)]`
`= 101.6 + 63.9/327.37 (T_2 - 273.16)`
or `T_2 = ((123.4-101.6)xx327.34)/63.9+ 273.16 = 111.67 + 273.16`
= 384.83 K
Solution 2
It is given that:
R = R0 [1 + α (T – T0)] … (i)
Where,
R0 and T0 are the initial resistance and temperature respectively
R and T are the final resistance and temperature respectively
α is a constant
At the triple point of water, T0 = 273.15 K
Resistance of lead, R0 = 101.6 Ω
At normal melting point of lead, T = 600.5 K
Resistance of lead, R = 165.5 Ω
Substituting these values in equation (i), we get:
`R = R_0[1+alpha(T - T_0)]`
`165.5=101.6 [1+alpha(600.5 - 273.15)]`
`1.629 = 1 + alpha(327.35)`
`:.alpha = 0.629/327.35 = 1.92 xx 10^(-3) K^(-1)`
For resistance, `R_1= 123.4 Omega`
`R_1 = R_0[1+alpha(T-T_0)]`
Where T is the temperrature when the resistance of lead is `123.4 Omega`
`123.4 = 101.6[]1+1.92 xx 10^(-3)(T-273.15)]`
`1.214 = 1 + 1.92 xx 10^(-3)(T - 273.15)`
`0.214/(1.92xx10^(-3)) = T - 273.15`
:. T = 384.61 K
RELATED QUESTIONS
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)?
Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.
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
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?
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.
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.
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?
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.
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 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 ball is dropped on a floor from a height of 2.0 m. After the collision it rises up to a height of 1.5 m. Assume that 40% of the mechanical energy lost goes as thermal energy into the ball. Calculate the rise in the temperature of the ball in the collision. Heat capacity of the ball is 800 J K−1.
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).
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.
At what temperature, the reading of a fahrenheit thermometer will be three times that of celsius thermometer?
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 ______.
Convert 37 °C (normal body temperature) to Kelvin.
Which of the following correctly describes an adiabatic wall?
