Advertisements
Advertisements
प्रश्न
Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and α = 1.7 × 10–5/°C, bulk modulus for copper = 140 × 109 N/m2.
Advertisements
उत्तर
According to the problem, decrease in temperature
(Δt) = 57 – 37 = 20°C
Coefficient of linear expansion
(α) = 1.7 × 10–5/°C
Bulk modulus for copper (B) = 140 × 109 N/m2
Coefficient of cubical expansion
(γ) = 3α = 5.1 × 10–5/°C
Let the initial volume of the cavity be V and its volume increases by ΔV due to increasing in temperature.
∴ `ΔV = γVΔt`
⇒ `(ΔV)/V = γΔt`
We know, B = `"Stress"/"Volume strain"`
∴ Thermal stress = `B xx ((ΔV)/V) = B(γΔT)`
= `B(3αΔT)` .....(∵ γ = 3α)
= 140 × 109 × 3 × 1.7 × 10–5 × 20
= 1.428 × 108 Nm–2
This is about 103 times of atmospheric pressure.
APPEARS IN
संबंधित प्रश्न
If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?
Is it possible for two bodies to be in thermal equilibrium if they are not in contact?
For a constant-volume gas thermometer, one should fill the gas at
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.
The density of water at 0°C is 0.998 g cm–3 and at 4°C is 1.000 g cm–1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.
Answer the following question.
What is thermal stress?
Answer the following question.
Give an example of the disadvantages of thermal stress in practical use?
A glass flask has a volume 1 × 10−4 m3. It is filled with a liquid at 30°C. If the temperature of the system is raised to 100°C, how much of the liquid will overflow? (Coefficient of volume expansion of glass is 1.2 × 10−5 (°C)−1 while that of the liquid is 75 × 10−5 (°C)−1).
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 metre scale made of a metal reads accurately at 25 °C. Suppose in an experiment an accuracy of 0.12 mm in 1 m is required, the range of temperature in which the experiment can be performed with this metre scale is ______.(coefficient of linear expansion of the metal is `20 xx 10^-6 / (°"C")`
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.)
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
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 ______.
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
| S.No. | l(m) | ∆T (C) | ∆l (m) |
| 1. | 2 | 10 | `4 xx 10^-4` |
| 2. | 1 | 10 | `4 xx 10^-4` |
| 3. | 2 | 20 | `2 xx 10^-4` |
| 4. | 3 | 10 | `6 xx 10^-4` |
If the first observation is correct, what can you say about observations 2, 3 and 4.
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 ______.
The increase in the dimensions of a body due to an increase in its temperature is called ______.
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 ______.
