Advertisements
Advertisements
Question
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?
Options
P1 > P2
P1 = P2
P1 < P2
data is insufficient.
Advertisements
Solution
P1 > P2
Explanation:
As we know that the pressure and the quantity of gas in the system are constants. Thus, by using the ideal gas equation
PV = nRT
V ∝ T .....(When n, P and R are constants)
`V_1/T_1` = constant
Or slope of graph is constant
`V = (nRT)/P`
`(dV)/(dT) = (nR)/P`
Or `(dV)/(dT)` increases when P decreases
Thus, `(dV)/(dT) ∝ 1/P`
This shows that slope P1 is smaller than P2.
APPEARS IN
RELATED QUESTIONS
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?
When you come out of a river after a dip, you feel cold. Explain.
Find the number of molecules of an ideal gas in a volume of 1.000 cm3 at STP.
A gas cylinder has walls that can bear a maximum pressure of 1.0 × 106 Pa. It contains a gas at 8.0 × 105 Pa and 300 K. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break.
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.
Use R = 8.3 J K-1 mol-1
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
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.
In an ideal gas, the molecules possess ______.
When a gas is heated, its temperature increases. Explain this phenomenon on the basis of the kinetic theory of gases.
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.
Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 105 N/m2.
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?
Why the temperature of all bodies remains constant at room temperature?
What is the microscopic origin of temperature?
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.
Consider a rectangular block of wood moving with a velocity v0 in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v0 is A. Show that the drag force on the block is `4ρAv_0 sqrt((KT)/m)`, where m is the mass of the gas molecule.
When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
