Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
Temperature at which rod is resting on a fixed horizontal base without any strain, T1=20 °C. Then the rod is heated to temperature, T2 = 50 °C
So change in temperature,ΔT =T2-T1=30°C
Coefficient of linear expansion of steel, α = 1.2 × 10–5 °C-1
Let L be the length of the rod without heating and L' be the length of the rod on heating.
Let longitudinal strain developed in the rod be S.
We know that
L' =L(1+∝ΔT)
⇒ ΔL =L∝ΔT
Strain, S = `(ΔL)/L`
`=(L∝ΔT)/L`
=αΔT
⇒ S =1.2 × 10-5 ×(50-20)
=1.2 × 10-5 ×30
=1.2 × 10-5 × 30
=36 × 10-5
S = 3.6 × 10-4
The strain of 3.6 × 10-4 will be opposite to the direction of expansion.
APPEARS IN
RELATED QUESTIONS
If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?
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.
Derive the relation between three coefficients of thermal expansion.
Answer the following question.
State applications of thermal expansion.
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).
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 sphere 10.01 cm in diameter is placed on a brass ring of internal diameter 10 cm and at the same temperature of 12° C. The temperature up to which they should be heated together so that the metal sphere just passes through the ring is `[alpha_"metal"= 12 xx 10^-6//°"C" and alpha_"brass" =18 xx 10^-6//°"C"]` ____________.
A metal rod of Young's moduls 'Y' and coefficient of linear expansion 'a' has its temeprature raised by 'Δ θ'. The linear stress to prevent the expansion of rod is ______.
(L and l is original length of rod and expansion respectively)
The volume of a metal block changes by 0.86% when heated through 200 °C then its coefficient of cubical expansion is ______.
As the temperature is increased, the time period of a pendulum ______.
At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both diameters have been measured at room temperature (27°C). (Given: coefficient of linear thermal expansion of gold αL = 1.4 × 10-5 K-1).
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)
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 ______.
Among solids, liquids, and gases, the thermal expansion on heating is ______.
