Advertisements
Advertisements
प्रश्न
Show that for diatomic gas the ratio of the two specific heats is 7:5.
Advertisements
उत्तर
- For a gas consisting of diatomic molecules such as O2, N2, CO, HCl, enclosed in a container held at a constant temperature T, if treated as a rigid rotator, each molecule will have 3 translational and 2 rotational degrees of freedom.
- According to the law of equipartition of energy, the internal energy of one mole of gas is,
E = `3/2"N"_"A""k"_"B""T" + 2/2"N"_"A""k"_"B""T"`
= `5/2"N"_"A""k"_"B""T"` - The molar specific heat at constant volume will be,
Cv = `5/2"N"_"A""k"_"B"`
= `5/2`R - Using Mayer’s relation,
Cp = R + Cv
∴ Cp = `7/2`R
∴ `"C"_"p"/"C"_"v" = 7/5`
APPEARS IN
संबंधित प्रश्न
Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres
The figure shows the plot of PV/T versus Pfor 1.00×10–3 kg of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true: T1 > T2 or T1 < T2?
(c) What is the value of PV/T where the curves meet on the y-axis?
(d) If we obtained similar plots for 1.00 ×10–3 kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot)? (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u, R = 8.31 J mo1–1 K–1.)
At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at – 20 °C? (atomic mass of Ar = 39.9 u, of He = 4.0 u).
Oxygen is filled in a closed metal jar of volume 1.0 × 10−3 m3 at a pressure of 1.5 × 105Pa and temperature 400 K. The jar has a small leak in it. The atmospheric pressure is 1.0 × 105 Pa and the atmospheric temperature is 300 K. Find the mass of the gas that leaks out by the time the pressure and the temperature inside the jar equalise with the surrounding.
During the practical session in the lab when hydrogen sulphide gas having offensive odour is prepared for some test, we can smell the gas even 50 metres away. Explain the phenomenon.
Give reasons for the following:
Gas fills the vessel completely in which it is kept.
Choose the correct answer:
The graph of PV vs P for gas is
Match the following:
|
|
Column A |
Column B |
|
(a) |
cm3 |
(i) Pressure |
|
(b) |
Kelvin |
(ii) Temperature |
|
(c) |
Torr |
(iii) Volume |
|
(d) |
Boyle's law |
(iv) `"V"/"T" = ("V"_1)/("T"_1)` |
|
(a) |
Charles's law |
(v) `"PV"/"T" = ("P"_1 "V"_1)/"T"_1` |
|
|
|
(vi) PV = P1V1 |
Fill in the blanks:
If the temperature is reduced to half, ………….. would also reduce to half.
A gas occupies 500 cm3 at a normal temperature. At what temperature will the volume of the gas be reduced by 20% of its original volume, the pressure is constant?
Correct the following statement:
0°C is equal to zero Kelvin.
Name or state the following:
The standard pressure of a gas in cm. of mercury corresponding to one atmospheric pressure.
Give reason for the following:
Volumes of gases are converted into s.t.p. conditions and then compared.
The average energy per molecule is proportional to ______
Gases exert pressure on the walls of the container because the gas molecules ______
The equation of state for 2g of oxygen at a pressure 'P' and temperature 'T', when occupying a volume 'V' will be ______.
Estimate the average thermal energy of a helium atom at room temperature (27 °C).
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic).
Do the vessels contain an equal number of respective molecules?
Which of the following diagrams (Figure) depicts ideal gas behaviour?
 (a) |
 (b) |
 (c) |
 (d) |
Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197g mole–1.
A box of 1.00 m3 is filled with nitrogen at 1.50 atm at 300K. The box has a hole of an area 0.010 mm2. How much time is required for the pressure to reduce by 0.10 atm, if the pressure outside is 1 atm.
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will ______.
At room temperature, a diatomic gas is found to have an r.m.s. speed of 1930 ms-1. The gas is ______.
P ∝ T at constant volume is the statement of ______.
