Advertisements
Advertisements
प्रश्न
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` .
उत्तर
Given :
`P = (p_0)/(1+(V/V_0)^2`
Multiplying both sides by V, we get
`pV = (p_0V)/(1+(V/V_0)^2)`
`pV = RT` [From eq. (1)]
Now ,
`RT = (p_0V)/(1+(V/V_0)^2)`
`T = 1/R ((p_0V_0)/(1+(V_0/V_0)^2))` [`V=V_0`]
⇒ `T = (p_0V_0)/(2R)`
APPEARS IN
संबंधित प्रश्न
A gas is kept in an enclosure. The pressure of the gas is reduced by pumping out some gas. Will the temperature of the gas decrease by Charles's low?
Answer in brief:
Compare the rms speed of hydrogen molecules at 127ºC with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
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.
Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.
Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.
Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) (c) λmax = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10-3 m.K).
Calculate the value of λmax for radiation from a body having a surface temperature of 3000 K. (b = 2.897 x 10-3 m K)
Why the temperature of all bodies remains constant at room temperature?
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
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) ____________.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure is ______.
The average translational kinetic energy of a molecule in a gas is 'E1'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E2'. The temperature at which E1 = E2 is possible, is ______.
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
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 rms speeds.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
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 ______.
Show that the average energy per molecule is proportional to the absolute temperature T of the gas.
