Advertisements
Advertisements
प्रश्न
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).
Advertisements
उत्तर
Given: V1 = 1 × 10−4 m3 = 10−4 m3, T1 = 30°C, T2 = 100°C, γglass = 1.2 × 10−5 , `γ_"liquid"` = 75 × 10−5
To find: Volume of liquid that overflows
Formula: `gamma = (V_2 - V_1)/(V_1(T_2 - T_1))`
Calculation: From formula,
Increase in volume = V2 − V1 = γ = V1(T2 − T1)
Increase in volume of glass
= γglass = V1(T2 − T1)
= 1.2 × 10−5 × 10−4 × (100 − 30)
= 1.2 × 70 × 10−9
= 8.4 × 10−8 m3
∴ Increase in volume of glass = 8.4 × 10−8 m3
Increase in volume of liquid -
= `γ_"liquid"`= V1(T2 − T1)
= 75 × 10−5 × 10-4 × (100 − 30)
= 75 × 70 × 10−9
= 5250 × 10−9 m3
∴ Increase in volume of liquid = 5250 × 10−9 m3
∴ Volume of liquid which overflows
= (5250 − 84) × 10−9 m3
= 5166 × 10−9 m3
= 0.5166 × 10−8 m3
∴ Volume of liquid that overflows is 0.5166 × 10−8 m3
APPEARS IN
संबंधित प्रश्न
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
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?
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.
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.
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.
Answer the following question.
What is thermal stress?
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 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 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 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 uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
An aluminium sphere is dipped into water. Which of the following is true?
As the temperature is increased, the time period of a pendulum ______.
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 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.
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temeprature is T + ΔT. Calculate the increase in the volume of the metal box.
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 ______.
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:
The increase in the dimensions of a body due to an increase in its temperature is called:
When a solid is heated, its atoms vibrate faster and move farther apart. This happens because:
