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
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
The average translational kinetic energy of air molecules is 0.040 eV (1 eV = 1.6 × 10−19J). Calculate the temperature of the air. Boltzmann constant k = 1.38 × 10−23 J K−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
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 adiabatic cylindrical tube of cross-sectional area 1 cm2 is closed at one end and fitted with a piston at the other end. The tube contains 0.03 g of an ideal gas. At 1 atm pressure and at the temperature of the surrounding, the length of the gas column is 40 cm. The piston is suddenly pulled out to double the length of the column. The pressure of the gas falls to 0.355 atm. Find the speed of sound in the gas at atmospheric temperature.
If a = 0.72 and r = 0.24, then the value of tr is ______.
Energy is emitted from a hole in an electric furnace at the rate of 20 W when the temperature of the furnace is 727°C. What is the area of the hole? (Take Stefan’s constant σ to be 5.7 × 10-8 Js-1 m-2K-4.)
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)
Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?
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?
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.
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 rms speeds.
An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.
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.
For a particle moving in vertical circle, the total energy at different positions along the path ______.
Assuming the expression for the pressure P exerted by an ideal gas, prove that the kinetic energy per unit volume of the gas is `3/2` P.
At what temperature will therms velocity of a gas be four times its value at STP?
Which of the following materials is diathermanous?
