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` .
Advertisements
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
If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
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
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
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.
The condition of air in a closed room is described as follows. Temperature = 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at 25°C − 3.2 kPa.
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
The power radiated by a perfect blackbody depends only on its ______
Calculate the energy radiated in one minute by a blackbody of surface area 200 cm2 at 127 °C (σ = 5.7 x 10-8 J m-2 s-1 K-4)
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
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 ______.
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 ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
If a = 0. 72 and r = 0.24, then the value of t is ______.
Which of the following materials is diathermanous?
