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?
Advertisements
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
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10–5 K–1.
If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead.
Answer the following question.
What is thermal stress?
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?
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 clock pendulum having coefficient of linear expansion. α = 9 × 10-7/°C-1 has a period of 0.5 s at 20°C. If the clock is used in a climate, where the temperature is 30°C, how much time does the clock lose in each oscillation? (g = constant)
A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is ______.
A hot body at a temperature 'T' is kept in a surrounding of temperature 'T0'. It takes time 't1' to cool from 'T' to 'T2', time t2 to cool from 'T2' to 'T3' and time 't3' to cool from 'T3' to 'T4'. If (T - T2) = (T2 - T3) = (T3 - T4), then ______.
A metal rod of length Land cross-sectional area A is heated through T °C. What is the force required to prevent the expansion of the rod lengthwise?
(Y = Young's modulus of material of the rod, α = coefficient of linear expansion of the rod.)
The volume of a metal block changes by 0.86% when heated through 200 °C then its coefficient of cubical expansion is ______.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.
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 clock with an iron pendulum keeps the correct time at 15°C. If the room temperature is 20°C, the error in seconds per day will be near ______.
(coefficient of linear expansion of iron is 1.2 × 10-5/°C)
A metal rod Y = 2 × 1012 dyne cm-2 of coefficient of linear expansion 1.6 × 10-5 per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is ______.
Which of the following correctly lists the three types of thermal expansion?
When a solid is heated, its atoms vibrate faster and move farther apart. This happens because ______.
