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
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.
If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?
If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?
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
For a constant-volume gas thermometer, one should fill the gas at
Answer the following question.
Derive the relation between three coefficients of thermal expansion.
Answer the following question.
State applications of thermal expansion.
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 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 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 hot body at a temperature 'T' is kept in a surrounding of temperature 'T0'. It takes time 't1' to cool from 'T' to 'T2', time t2 to cool from 'T2' to 'T3' and time 't3' to cool from 'T3' to 'T4'. If (T - T2) = (T2 - T3) = (T3 - T4), then ______.
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 ______.
A bimetallic strip is made of aluminium and steel (αAl > αsteel) . On heating, the strip will ______.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
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.
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.
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).
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)
