Advertisements
Advertisements
Question
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?
Solution 1
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
Solution 2
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
RELATED QUESTIONS
If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?
Answer the following question.
Give an example of the disadvantages of thermal stress in practical use?
Solve the following problem.
In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?
An iron plate has a circular hole of a diameter 11 cm. Find the diameter of the hole when the plate is uniformly heated from 10° C to 90° C.`[alpha = 12 xx 10^-6//°"C"]`
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
As the temperature is increased, the time period of a pendulum ______.
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new temperature is T + ∆T. The increase in the volume of the sphere is approximately ______.
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.
A metal ball immersed in water weighs w1 at 0°C and w2 at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then ______.
A glass flask is filled up to a mark with 50 cc of mercury at 18°C. If the flask and contents are heated to 38°C, how much mercury will be above the mark? (α for glass is 9 × 10-6/°C and coefficient of real expansion of mercury is 180 × 10-6/°C)
