Advertisements
Advertisements
प्रश्न
Figure shows two rigid vessels A and B, each of volume 200 cm3, containing an ideal gas (Cv = 12.5 J K−1 mol−1). The vessels are connected to a manometer tube containing mercury. The pressure in both the vessels is 75 cm of mercury and the temperature is 300 K. (a) Find the number of moles of the gas in each vessel. (b) 5.0 J of heat is supplied to the gas in vessel A and 10 J to the gas in vessel B. Assuming there's no appreciable transfer of heat from A to B, calculate the difference in the heights of mercury in the two sides of the manometer. Gas constant, R = 8.3 J K−1 mol−1.
Advertisements
उत्तर
Given:
Volume of gas in each vessel, V = 200 cm3
Specific heat at constant volume of the gas, Cv = 12.5 J/mol-K
Initial temperature of the gas, T = 300 K
Initial pressure of the gas, P = 75 cm of Hg
(a) Using the ideal gas equation, number of moles of gases in each vessel,
75 cm of Hg = 99991.5 N/m2
`"n" = ("P""V")/("R""T")`
`= (99991.5 xx 200 xx 10^-6)/(8.3 xx 300)`
= 8031.4 xx 10-6
=0.008
(b) Heat is supplied to the gas, but dV is zero as the container has rigid walls.
So, dW = P Δ V = 0
From first law of thermodynamics,
dQ = dU
⇒ 5 = nCvdT
⇒ 5 = 0.008 × 12.5 × dT
⇒ dT = 50 for A
`"P"/"T" = "P"_"A"/"T"_"A" ` because volume is kept constant.
Q = nCvdT
`"T" = "Q"/("n""C"_"v")`
`75/300 =( "P"_"A" xx 0.008 xx 12.5)/5`
`"P"_"A" = (75 xx 5)/(300 xx 0.008 xx 12.5)`
= 12.5 cm of Hg
Again ,` "P"/"T" = "P"_"B"/"T"_"B" [ For container B]`
`75/300 =( "P"_"B" xx 0.008 xx 12.5 )/10`
PB = 25 cm of Hg
The distance moved by the mercury,
PB − PA = 25 − 12.5 = 12.5 cm
APPEARS IN
संबंधित प्रश्न
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.
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
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
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)`.
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 ?
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.
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.
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?
In an ideal gas, the molecules possess ______.
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
The power radiated by a perfect blackbody depends only on its ______
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?
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
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?
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.
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 ______.
Show that the average energy per molecule is directly proportional to the absolute temperature ‘T’ of the gas.
