Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:-
Mass of aluminium = 0.5 kg
Mass of water = 0.2 kg
Mass of iron = 0.2 kg
Specific heat of aluminium = 910 J kg−1 K−1
Specific heat of iron = 470 J kg−1 K−1
Specific heat of water = 4200 J kg−1 K−1
Let the equilibrium temperature of the mixture be T.
Temperature of aluminium and water = 20°C = 273+20 = 293 K
Temperature of iron = 100°C = 273 + 100 = 373 K
Heat lost by iron, H1 = 0.2 × 470 × (373 − T)
Heat gained by water = 0.2 × 4200 × (T − 293)
Heat gained by aluminium = 0.5 × 910 × (T−293)
Total heat gained by water and iron, H2 = 0.5 × 910 (T−293) + 0.2 × 4200 × (T − 293)
H2 = (T − 293) [0.5 × 910 + 0.2 × 4200]
We know,
Heat gain = Heat lost
⇒ (T − 293) [0.5 × 910 + 0.2 × 4200] = 0.2 × 470 × (373 −T)
⇒ (T − 293) (455 + 840) = 94 (373 − T)
`rArr(T-293)1295/94=(373-T)`
`(T-293)xx14=(373-T)`
⇒ 14 T − 293 × 14 = 373 − T
⇒ 15 T = 373 + 4102 = 4475
`rArrT=4475/15=298.33Kapprox298K`
∴ T = (298 − 273)°C = 25°C
∴ Final temperature = 25°C
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.
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?
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?
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
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.
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?
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 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.
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 metal block of density 600 kg m−3 and mass 1.2 kg is suspended through a spring of spring constant 200 N m−1. The spring-block system is dipped in water kept in a vessel. The water has a mass of 260 g and the bloc is at a height 40 cm above the bottom of the vessel. If the support of the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is 250 J kg−3 K−1 and that of water is 4200 J kg−1 K−1. Heat capacities of the vessel and the spring are negligible.
At what temperature, the reading of a fahrenheit thermometer will be three times that of celsius thermometer?
The Zeroth Law of Thermodynamics is the basis for which of the following?
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 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?
Which of the following is NOT a characteristic of a good thermometer?
