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
A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0 × 10–5 K–1, steel = 1.2 × 10–5 K–1).
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?
A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z
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.
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.
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?
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)
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 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 ______.
The volume of a metal block changes by 0.86% when heated through 200 °C then its coefficient of cubical expansion is ______.
If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.
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 ______.
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
- Assertion A: When a rod lying freely is heated, no thermal stress is developed in it.
- Reason R: On heating, the length of the rod increases. In light of the above statements.
choose the correct answer from the options given below:
When heat is given to a substance, it generally ______.
Which of the following correctly lists the three types of thermal expansion?
Among solids, liquids, and gases, the thermal expansion on heating is ______.
