Advertisements
Advertisements
प्रश्न
The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?
Advertisements
उत्तर १
Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1
Rise in temperature, ΔT = 30°C
Fractional change in its volume =`(triangle V)/V`
This change is related with the change in temperature as:
`(triangle V)/V = alpha_V triangle T`
`V_(T_2) - V_(T_1) = V_(T_1) alpha_V triangle T`
`m/rho_(T_2) - m/rho_(T_1) = m/rho_(T_1) alpha_1 triangleT`
Where,
m = Mass of glycerine
`rho_(T_1)` = Initial density at `T_1`
`rho_(T_2)` = Final density at `T_2`
`(rho_(T_1) - rho_(T_2))/rho_(T_2) = alpha_1 triangle T`
Where
`(rho_(T_1) - rho_(T_2_))/(rho_T_2)` = = Fractional change in density
∴Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2
उत्तर २
Here `gamma= 49 xx 10^(-5) ""^@C^(-1)`, `triangle T = 30 ""^@C`
As` V = V + triangle V = V(1+gamma triangle T)`
`V' = V(1+49xx10^(-5)xx30) = 1.0147 V`
Since `rho = m/V, rho^n = m/(V') = m/1.0147V = 0.9855 rho`
Fractional change in density = `(rho - rho')/rho`
`= (rho - 0.9855 rho)/rho = 0.0145`
APPEARS IN
संबंधित प्रश्न
A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1
If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.
Is it possible for two bodies to be in thermal equilibrium if they are not in contact?
A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C.
Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10–5 °C–1.
Show that the moment of inertia of a solid body of any shape changes with temperature as I = I0 (1 + 2αθ), where I0 is the moment of inertia at 0°C and α is the coefficient of linear expansion of the solid.
Answer the following question.
State applications of thermal expansion.
Solve the following problem.
A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the wooden rim and the iron ring are 1.5 m and 1.47 m respectively at room temperature of 27 °C. To what temperature the iron ring should be heated so that it can fit the rim of the wheel? (αiron = 1.2 × 10–5K–1).
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
An aluminium sphere is dipped into water. Which of the following is true?
Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion α) about its perpendicular bisector when its temperature is slightly increased by ∆T.
The height of mercury column measured with brass scale at temperature T0 is H0. What height H' will the mercury column have at T = 0°C. Coefficient of volume expansion of mercury is γ. Coefficient of linear expansion of brass is α ______.
An anisotropic material has coefficient of linear thermal expansion α1, α2 and α3 along x, y and z-axis respectively. Coefficient of cubical expansion of its material will be equal to ______.
If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be ______.
A solid metallic cube having a total surface area of 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in the volume of the cube.
(Given: α = 5.0 × 10−4°C−1)
The increase in the dimensions of a body due to an increase in its temperature is called ______.
Among solids, liquids, and gases, the thermal expansion on heating is ______.
The volume of a block of metal at 30°C changes by 0.12% when its temperature is increased to 70°C. The coefficient of linear expansion of the metal is ______.
