Advertisements
Advertisements
प्रश्न
The densities of wood and benzene at 0°C are 880 kg m3 and 900 kg m–3 , respectively. The coefficients of volume expansion are 1.2 × 10–3 °C–1 for wood and 1.5 × 10–3 °C–1for benzene. At what temperature will a piece of wood just sink in benzene?
Advertisements
उत्तर
Given:
Density of wood at 0 °C, fw = 880 kgm-3
Density of benzene at 0 °C, fb = 900 kgm-3
Coefficient of volume expansion for wood, γw = Coefficient of volume expansion for benzene, γb = 1.5 × 10–3 °C–1
So, initial temperature, T1 = 0 °C
Let T2 be the temperature at which the piece of wood will just sink in benzene and ΔT = T2-T1.
The piece of wood begins to sink when its weight is equal to the weight of the benzene displaced.
Mass = volume × density
Therefore, Vfwg = Vfbg
`=> f_w/(1+γ_w ΔT) = f_b/(1+γ_bΔT)`
`=> 880/(1+1.2×10^-3ΔT) = 900/(1+1.5×10^-3ΔT)`
⇒ 880+880 × 1.5 × 10-3 ΔT =900+900 ×1.2×10-3 ΔT
⇒ (1320 -1080)× 10-3 ΔT =20
⇒ ΔT = 83.3°C
⇒ T2 -T1 ≅ 83°
⇒ T2 -0° ≅ 83°
⇒ T2 ≅ 83°C
Therefore, the piece of wood will just sink in benzene at 83 oC.
APPEARS IN
संबंधित प्रश्न
Define emissive power and coefficient of emmision of a body.
A metal ball cools from 64 °C to 50 °C in 10 minutes and to 42 °C in next 10 minutes. The ratio of rates of fall of temperature during the two intervals is _______.
Answer the following:
There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale?
What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?
The substance which allows heat radiations to pass through is _______.
(A) iron
(B) water vapour
(C) wood
(D) dry air
Does the temperature of a body depend on the frame from which it is observed?
A spherical shell is heated. The volume changes according to the equation Vθ = V0 (1 + γθ). Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell?
An aluminium sphere is dipped into water at 10°C. If the temperature is increased, the force of buoyancy
A concrete slab has a length of 10 m on a winter night when the temperature is 0°C. Find the length of the slab on a summer day when the temperature is 35°C. The coefficient of linear expansion of concrete is 1.0 × 10–5 °C–1.
A metre scale made of steel is calibrated at 20°C to give correct reading. Find the distance between the 50 cm mark and the 51 cm mark if the scale is used at 10°C. Coefficient of linear expansion of steel is 1.1 × 10–5 °C–1.
A pendulum clock shows correct time at 20°C at a place where g = 9.800 m s–2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g = 9.788 m s–1. At what temperature will the clock show correct time? Coefficient of linear expansion of steel = 12 × 10–6 °C–1.
A steel wire of cross-sectional area 0.5 mm2 is held between two fixed supports. If the wire is just taut at 20°C, determine the tension when the temperature falls to 0°C. Coefficient of linear expansion of steel is 1.2 × 10–5 °C–1 and its Young's modulus is 2.0 × 10–11 Nm–2.
Define one mole.
Heat is measured in Celsius or centigrade.
Give reasons for the following:
Hot metal ball of 80° C is dipped into water of 80°C. The ball will not contract.
The degree of hotness and coldness of a body is called ______.
An earthen pitcher loses 1 gm of water per minute due to evaporation. If the water equivalent of the pitcher is 0.5 kg and the pitcher contains 9.5 kg of water, calculate the time required for the water in a pitcher to cool to 28°C from the original temperature of 30°C. Neglect radiation effects. The latent heat of vaporization in this range of temperature is 580 Cal/gm and the specific heat of water is 1 Cal/gm°C.
Which state of matter has particles that vibrate about fixed equilibrium positions?
