Advertisements
Advertisements
प्रश्न
The average translational kinetic energy of air molecules is 0.040 eV (1 eV = 1.6 × 10−19J). Calculate the temperature of the air. Boltzmann constant k = 1.38 × 10−23 J K−1.
Advertisements
उत्तर
We know from kinetic theory of gases that the average translational energy per molecule is \[\frac{3}{2}kT\].
Now,
Eavg= 0.040 eV = \[0.040 \times 1 . 6 \times {10}^{- 19} = 6 . 4 \times {10}^{- 21} J\]
\[6 . 40 \times {10}^{- 21} = \frac{3}{2} \times 1 . 38 \times {10}^{- 23} \times T\]
\[ \Rightarrow T = \frac{2}{3} \times \frac{6 . 40 \times {10}^{- 21}}{1 . 38 \times {10}^{- 23}} = 309 . 2 \text { K }\]
APPEARS IN
संबंधित प्रश्न
Can we define the temperature of (a) vacuum, (b) a single molecule?
Which of the following parameters is the same for molecules of all gases at a given temperature?
The process on an ideal gas, shown in figure, is
A gas cylinder has walls that can bear a maximum pressure of 1.0 × 106 Pa. It contains a gas at 8.0 × 105 Pa and 300 K. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break.
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.
Use R = 8.3 J K-1 mol-1
An ideal gas is trapped between a mercury column and the closed-end of a narrow vertical tube of uniform base containing the column. The upper end of the tube is open to the atmosphere. The atmospheric pressure equals 76 cm of mercury. The lengths of the mercury column and the trapped air column are 20 cm and 43 cm respectively. What will be the length of the air column when the tube is tilted slowly in a vertical plane through an angle of 60°? Assume the temperature to remain constant.
Figure shows a cylindrical tube of cross-sectional area A fitted with two frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the temperature of the gas is T0 and its pressure is p0 which equals the atmospheric pressure. (a) What is the tension in the wire? (b) What will be the tension if the temperature is increased to 2T0 ?
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
A glass contains some water at room temperature 20°C. Refrigerated water is added to it slowly. when the temperature of the glass reaches 10°C, small droplets condense on the outer surface. Calculate the relative humidity in the room. The boiling point of water at a pressure of 17.5 mm of mercury is 20°C and at 8.9 mm of mercury it is 10°C.
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.
The average translational kinetic energy of gas molecules depends on ____________.
What is the microscopic origin of temperature?
The graph of kinetic energy against the frequency v of incident light is as shown in the figure. The slope of the graph and intercept on X-axis respectively are ______.
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
At what temperature will therms velocity of a gas be four times its value at STP?
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
