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
When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?
If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?
The mean square speed of the molecules of a gas at absolute temperature T is proportional 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
The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15°C, what will be the new dew point?
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.
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.
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?
The average translational kinetic energy of gas molecules depends on ____________.
When photons of energy hv fall on a metal plate of work function 'W0', photoelectrons of maximum kinetic energy 'K' are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be ______.
A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity `omega`. Its kinetic energy is ______.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure is ______.
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?
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of average K.E.
Assuming the expression for the pressure P exerted by an ideal gas, prove that the kinetic energy per unit volume of the gas is `3/2` P.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
If a = 0. 72 and t = 0.04, then the value of r is ______.
