Advertisements
Advertisements
प्रश्न
The molecules of a given mass of a gas have root mean square speeds of 100 ms−1 at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?
Advertisements
उत्तर
We know that for a given mass of a gas
`V_(rms) = sqrt((3RT)/M)`
Where R is gas constant
T is the temperature in Kelvin
M is the molar mass of the gas
Clearly, `V_(rms) ∝ sqrt(T)`
As R and M are constants,
`(V_(rms))_1/(V_(rms))_2 = sqrt(T_1/T_2)`
Given, `(V_(rms))_1` = 100 m/s
T1 = 27°C = 27 + 273 = 300 K
T2 = 127°C = 127 + 273 = 400 K
∴ From equation (i)
`100/((V_(rms))_2) = sqrt(300/400) = sqrt(3)/2`
⇒ `(V_(rms))_2 = (2 xx 100)/sqrt(3) = 200/sqrt(3)` m/s
APPEARS IN
संबंधित प्रश्न
Which of the following parameters is the same for molecules of all gases at a given temperature?
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The mean speed of the molecules of a hydrogen sample equals the mean speed of the molecules of a helium sample. Calculate the ratio of the temperature of the hydrogen sample to the temperature of the helium sample.
Use R = 8.314 JK-1 mol-1
One mole of an ideal gas undergoes a process `P = (P_0)/(1+(V/V_0)^2` where `p_0` and `V_0` are constants . Find the temperature of the gas when `V=V_0` .
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.
An adiabatic cylindrical tube of cross-sectional area 1 cm2 is closed at one end and fitted with a piston at the other end. The tube contains 0.03 g of an ideal gas. At 1 atm pressure and at the temperature of the surrounding, the length of the gas column is 40 cm. The piston is suddenly pulled out to double the length of the column. The pressure of the gas falls to 0.355 atm. Find the speed of sound in the gas at atmospheric temperature.
Compare the rms speed of hydrogen molecules at 127°C with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 105 N/m2.
Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?
Earth’s mean temperature can be assumed to be 280 K. How will the curve of blackbody radiation look like for this temperature? Find out λmax. In which part of the electromagnetic spectrum, does this value lie? (Take Wien's constant b = 2.897 × 10−3 m K)
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 ______.
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
The average translational kinetic energy of a molecule in a gas becomes equal to 0.49 eV at a temperature about (Boltzmann constant = 1.38 x 10-23 JK-1) ____________.
For a particle moving in vertical circle, the total energy at different positions along the path ______.
When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.
At what temperature will therms velocity of a gas be four times its value at STP?
If a = 0. 72 and r = 0.24, then the value of t is ______.
