Advertisements
Advertisements
प्रश्न
An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.
Advertisements
उत्तर
Since the container is suddenly stopped which is initially moving with velocity v0, there is no time for the exchange of heat in the process.
The total KE of the container is transferred to gas molecules in the form of translational KE, thereby increasing the absolute temperature.
Let n be the no. of moles of the monoatomic gas in the container. Since the molar mass of the gas is m.
The total mass of the container, M = mn
KE of molecules due to velocity v0,
KE = `1/2 (mn) v_0^2` ......(i)
Final KE of gas = 0
Change in kinetic energy, `ΔK = 1/2 (nm)v^2`
If ΔT = Change in absolute temperature,
Then the internal energy of the gas
`ΔU = nC_vΔT = n(3/2 R)ΔT` .....(ii)
According to the conservation of mechanical energy, we get
ΔK = ΔU
By equations (i) and (ii), we get
⇒ `1/2 (mn)v_0^2 = n 3/2 R(ΔT)`
`(mn)v_0^2 = n3R(ΔT)`
⇒ ΔT = `((mn)v_0^2)/(3nR) = (mv_0^2)/(3R)`
APPEARS IN
संबंधित प्रश्न
Can we define the temperature of (a) vacuum, (b) a single molecule?
Find the number of molecules of an ideal gas in a volume of 1.000 cm3 at STP.
0.040 g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12 J.
Use R = 8.3 J K-1 mol-1
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.
Answer in brief:
What will happen to the mean square speed of the molecules of a gas if the temperature of the gas increases?
Answer in brief:
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.
In an ideal gas, the molecules possess ______.
If the density of oxygen is 1.44 kg/m3 at a pressure of 105 N/m2, find the root mean square velocity of oxygen molecules.
Calculate the average molecular kinetic energy
- per kmol
- per kg
- per molecule
of oxygen at 127°C, given that the molecular weight of oxygen is 32, R is 8.31 J mol−1K−1 and Avogadro’s number NA is 6.02 × 1023 molecules mol−1.
The emissive power of a sphere of area 0.02 m2 is 0.5 kcal s-1m-2. What is the amount of heat radiated by the spherical surface in 20 seconds?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
Average kinetic energy of H2 molecule at 300K is 'E'. At the same temperature, average kinetic energy of O2 molecule will be ______.
Explain why there is no atmosphere on moon.
23Ne decays to 23Na by negative beta emission. Mass of 23Ne is 22.994465 amu mass of 23Na is 22.989768 amu. The maximum kinetic energy of emitted electrons neglecting the kinetic energy of recoiling product nucleus is ______ MeV.
A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is ______.
When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms-1 to vs, and Then vs is ______.
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?
Which of the following materials is diathermanous?
