Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
When you come out of a river after a dip, you feel cold. Explain.
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The process on an ideal gas, shown in figure, is
Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated and it is found that the cork pops out when the temperature reaches 600 K. Let dN denote the magnitude of the normal contact force exerted by a small length dlof the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate `(dN)/(dt)`.
The weather report reads, "Temperature 20°C : Relative humidity 100%". What is the dew point?
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:
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.
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 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.
When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
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 ______.
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.
Explain why there is no atmosphere on moon.
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 ______.
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 ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
