Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given: T1 = 27 °C, T2 = 45 °C, L1 = 10 m. α = 1.2 × 10–5 / K
To find: Gap that should be left (L2 – L1)
Formula: L2 – L1 = L1 α (T2 - T1)
Calculation: From formula,
L2 - L1 = 10 × 1.2 × 10–5 × (45 - 27)
= 2.16 × 10–3 m
= 2.16 mm
The gap that should be left between rail sections is 2.16 mm.
APPEARS IN
RELATED QUESTIONS
A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings Specific heat of aluminium = 0.91 J g–1 K–1
If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.
Is it possible for two bodies to be in thermal equilibrium if they are not in contact?
Answer the following question.
Derive the relation between three coefficients of thermal expansion.
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).
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 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)
A metal rod of cross-sectional area 3 × 10-6 m2 is suspended vertically from one end has a length 0.4 m at 100°C. Now the rod is cooled upto 0°C, but prevented from contracting by attaching a mass 'm' at the lower end. The value of 'm' is ______.
(Y = 1011 N/m2, coefficient of linear expansion = 10-5/K, g = 10m/s2)
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 ______.
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 rail track made of steel having length 10 m is clamped on a raillway line at its two ends (figure). On a summer day due to rise in temperature by 20° C, it is deformed as shown in figure. Find x (displacement of the centre) if αsteel = 1.2 × 10–5/°C.
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 ______.
A disc is rotating freely about its axis. The percentage change in angular velocity of a disc if temperature decreases by 20°C is ______.
(coefficient of linear expansion of material of disc is 5 × 10-4/°C)
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:
A solid metallic cube having a total surface area of 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in the volume of the cube.
(Given: α = 5.0 × 10-4°C-1)
Which of the following correctly lists the three types of thermal expansion?
Among solids, liquids, and gases, the thermal expansion on heating is:
