Advertisements
Advertisements
प्रश्न
An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
Advertisements
उत्तर १
Volume of the air bubble, V1 = 1.0 cm3 = 1.0 × 10–6 m3
Bubble rises to height, d = 40 m
Temperature at a depth of 40 m, T1 = 12°C = 285 K
Temperature at the surface of the lake, T2 = 35°C = 308 K
The pressure on the surface of the lake:
P2 = 1 atm = 1 ×1.013 × 105 Pa
The pressure at the depth of 40 m:
P1 = 1 atm + dρg
Where,
ρ is the density of water = 103 kg/m3
g is the acceleration due to gravity = 9.8 m/s2
∴P1 = 1.013 × 105 + 40 × 103 × 9.8 = 493300 Pa
We have : `(P_1V_1)/T_1 = (P_2V_2)/T_2`
Where, V2 is the volume of the air bubble when it reaches the surface
`V_2 = (P_1V_1T_2)/(T_1P_2)`
`= ((493300)(1.0 xx 10^(-6))308)/(285 xx 1.013 xx 10^5)`
= 5.263 × 10–6 m3 or 5.263 cm3
Therefore, when the air bubble reaches the surface, its volume becomes 5.263 cm3
उत्तर २
Volume of the bubble inside, `V_1 = 1.0 cm^3 = 1xx10^(-6) m^3`
Pressure on the bubble, `P_1` = Pressure of water + Atmospheric pressure
= `pgh + 1.01 xx 10^5 = 1000 xx 9.8 xx 40 + 1.01 xx 10^5`
`=3.92 xx 10^5 + 1.01 xx 10^5 = 4.93 xx 10^5` Pa
Temperature, `T_1 = 12 ^@C = 273 + 12 = 285 K`
Also, pressure outside the lake, `P_2 = 1.01 xx 10^5 n m^(-2)`
Temperature, `T_2 = 35 ^@C = 273 + 35 = 308` K, Volume `V_2` = ?
Now `(P_1V_1)/T_1 = (P_2V_2)/T_2`
`:. V_2 = (P_1V_1)/T_1. T_2/P_2 = (4.93xx10^5xx1xx10^(-6)xx 308)/(285 xx 1.01 xx 10^5) = 5.3 xx 10^(-6) m^(-3)`
संबंधित प्रश्न
Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3Å.
Consider a collision between an oxygen molecule and a hydrogen molecule in a mixture of oxygen and hydrogen kept at room temperature. Which of the following are possible?
(a) The kinetic energies of both the molecules increase.
(b) The kinetic energies of both the molecules decrease.
(c) kinetic energy of the oxygen molecule increases and that of the hydrogen molecule decreases.
(d) The kinetic energy of the hydrogen molecule increases and that of the oxygen molecule decreases.
Consider a mixture of oxygen and hydrogen kept at room temperature. As compared to a hydrogen molecule an oxygen molecule hits the wall
Calculate the mass of 1 cm3 of oxygen kept at STP.
The density of an ideal gas is 1.25 × 10−3 g cm−3 at STP. Calculate the molecular weight of the gas.
Use R=8.31J K-1 mol-1
Consider a sample of oxygen at 300 K. Find the average time taken by a molecule to travel a distance equal to the diameter of the earth.
Use R=8.314 JK-1 mol-1
Figure shows a vessel partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part equals the mean speed of the molecules in the right part. Calculate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.
Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10−5 cm.
Use R = 8.31 JK−1 mol−1
Hydrogen gas is contained in a closed vessel at 1 atm (100 kPa) and 300 K. (a) Calculate the mean speed of the molecules. (b) Suppose the molecules strike the wall with this speed making an average angle of 45° with it. How many molecules strike each square metre of the wall per second?
Use R = 8.31 JK-1 mol-1
A vertical cylinder of height 100 cm contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to 75 cm of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston.
The ratio Cp / Cv for a gas is 1.29. What is the degree of freedom of the molecules of this gas?
Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CAand CB be the molar heat capacities for the two processes,
For a solid with a small expansion coefficient,
Let Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?
70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
The figure shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.
The molar heat capacity for the process shown in the figure is
The molar heat capacity of oxygen gas at STP is nearly 2.5 R. As the temperature is increased, it gradually increases and approaches 3.5 R. The most appropriate reason for this behaviour is that at high temperatures
A sample of an ideal gas (γ = 1.5) is compressed adiabatically from a volume of 150 cm3 to 50 cm3. The initial pressure and the initial temperature are 150 kPa and 300 K. Find (a) the number of moles of the gas in the sample (b) the molar heat capacity at constant volume (c) the final pressure and temperature (d) the work done by the gas in the process and (e) the change in internal energy of the gas.
