Advertisements
Advertisements
Question
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
Advertisements
Solution
Applying equation of state of an ideal gas, we get
PV = nRT
⇒ P = \[\frac{nRT}{V} . . . 1 \]
Taking differentials, we get
⇒ PdV + VdP = nRdT . . . 2
Applying the additional law, we get
PV2 = c
V2 dP + 2VPdV = 0
⇒ VdP + 2PdV = 0 . . . 3
Subtracting eq. (3) from eq. (2) , we get
PdV = -nRdT
⇒ dV = \[\ {-}\frac{nR}{P}dT \]
Now ,
⇒ dV = \[\ {-}\frac{V}{T}dT \] [From eq. (1}]
⇒ \[\frac{dV}{V} = {-}\frac{dT}{T} \]
Integrating between T2 and T1 , we get
⇒ \[\int\limits_{V_1}^{2V} = {-}\int\limits_{T_1}^{T_2}\]
⇒ ln( 2V) - ln(V) = ln (T1) - ln (T2)
⇒ `ln ((2V)/V)` = `ln ((T_1)/(T_2))`
⇒ `T_2 = T_1/2`
APPEARS IN
RELATED QUESTIONS
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?
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?
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The temperature and pressure at Simla are 15.0°C and 72.0 cm of mercury and at Kalka these are 35.0°C and 76.0 cm of mercury. Find the ratio of air density at Kalka to the air density at Simla.
Use R=8.314J K-1 mol-1
Figure shows a cylindrical tube of cross-sectional area A fitted with two frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the temperature of the gas is T0 and its pressure is p0 which equals the atmospheric pressure. (a) What is the tension in the wire? (b) What will be the tension if the temperature is increased to 2T0 ?
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?
If a = 0.72 and r = 0.24, then the value of tr is ______.
Answer in brief:
What will happen to the mean square speed of the molecules of a gas if the temperature of the gas increases?
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 in detail the kinetic interpretation of temperature.
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 ______.
A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.
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?
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 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 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 ______.
If a = 0. 72 and t = 0.04, then the value of r is ______.
If a = 0. 72 and r = 0.24, then the value of t is ______.
