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 hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 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
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.
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.
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.
Give an example of the disadvantages of thermal stress in practical use?
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 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)
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 ______.
An aluminium sphere is dipped into water. Which of the following is true?
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.
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.
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 ______.
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)
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 ______.
When heat is given to a substance, it generally ______.
Among solids, liquids, and gases, the thermal expansion on heating is ______.
A metallic bar of Young’s modulus, 0.5 × 1011 N m−2 and coefficient of linear thermal expansion 10−5°C−1, length 1 m and area of cross-section 10−3 m2 is heated from 0°C to 100°C without expansion of bending. The compressive force developed in it is ______.
