Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर १
a)
Triple point of water, T = 273.16 K.
At this temperature, pressure in thermometer A, PA = 1.250 × 105 Pa
Let T1 be the normal melting point of sulphur.
At this temperature, pressure in thermometer A, P1 = 1.797 × 105 Pa
According to Charles’ law, we have the relation:
`P_A/T = P_1/T_1`
`:. T_1 =( P_1T)/P_A = (1.797 xx 20^(5) xx 273.16)/(1.250xx10^5)`
= 392.69 K
Therefore, the absolute temperature of the normal melting point of sulphur as read by thermometer A is 392.69 K.
At triple point 273.16 K, the pressure in thermometer B, PB = 0.200 × 105 Pa
At temperature T1, the pressure in thermometer B, P2 = 0.287 × 105 Pa
According to Charles’ law, we can write the relation:
`P_B/T = P_1/T_1`
`(0.200xx10^5)/273.16 = (0.287 xx 10^5)/T_1`
`:. T_1 = (0.287xx10^5)/(0.200xx10^5) xx 273.16 = 391.98 K`
Therefore, the absolute temperature of the normal melting point of sulphur as read by thermometer B is 391.98 K.
b) The oxygen and hydrogen gas present in thermometers A and B respectively are not perfect ideal gases. Hence, there is a slight difference between the readings of thermometers A and B.
To reduce the discrepancy between the two readings, the experiment should be carried under low pressure conditions. At low pressure, these gases behave as perfect ideal gases.
उत्तर २
Let T be the melting point of sulphur for thermometer A
`P_"tr" = 1.250 xx 10^5 Pa`; `P = 1.797 xx 10^5 Pa`
Now `T_A = T_(tr) xx P/P_"tr"`
`T_A = (273.16 xx 1.797 xx 10^5)/(.250xx10^5)k = 392.69 K`
For thermometer b
`P_"tr" = 0.200 xx 10^5 Pa`; `P = 0.287 xx 10^5 `Pa
`T_B = = T_"tr" xx P/P_"tr" = (273.16 xx 0.287 xx 10^5)/(0.200xx10^5) K`
b) The value of the melting point of sulphur found from the two thermometers differ slightly due to the reason that in practice, the gases do not behave strictly as perfect gases i.e., gases are not perfectly ideal.
To reduce the discrepency, readings should be taken for lower and lower pressures and the plot between temperature measured versus absolute pressure of the gas at triple point should be extrapolated to obtain the temperature in the limit pressure tends to zero (if P —> 0), when the gases approach ideal gas behaviour.
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)?
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.
Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
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)?
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.
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.
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.
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 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 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 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?
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.
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.
