Q15 of 26 Page 294

Given below are observations on molar specific heats at room temperature of some common gases.































Gas



Molar specific heat (Cv) (cal mo1–1 K–1)



Hydrogen



4.87



Nitrogen



4.97



Oxygen



5.02



Nitric oxide



4.99



Carbon monoxide



5.01



Chlorine



6.17



The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?

The gases given in the given table are diatomic. Besides the translational degree of freedom, they have other degrees of freedom. Heat must be supplied to increase the temperature of these gases. This increases the average energy of all the degrees of freedom. Hence, the molar specific heat of diatomic gases is more than that of monatomic gases. If only rotational mode of motion is considered, then the molar specific heat of a diatomic gas is equal to (5/2)R (where, R = Ideal gas law constant = 1.98 cal mol-1 K-1)

So, molar specific heat = (5/2) × 1.98 = 4.95 cal mol-1 K-1


With the exception of chlorine, all the observations in the given table agree with this value of molar specific heat. This is because of the fact that at room temperature, chlorine also has vibrational modes of motion besides rotational and translational modes of motion.


NOTE: Molecular degrees of freedom refer to the number of ways a molecule in the gas phase may move, rotate, or vibrate in space.


The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.


More from this chapter

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13

A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = 0.39 J g–1 K–1; heat of fusion of water

= 335 J g–1).

 14

In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at 150 °C is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing 150 cm3 of water at 27 °C. The final temperature is 40 °C. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for specific heat of the metal?

 16

Answer the following questions based on the P-T phase diagram of carbon dioxide:

(a) At what temperature and pressure can the solid, liquid and vapour phases of CO2 co-exist in equilibrium?


(b) What is the effect of decrease of pressure on the fusion and boiling point of


CO2?


(c) What are the critical temperature and pressure for CO2? What is their significance?


(d) Is CO2 solid, liquid or gas at (a) –70 °C under 1 atm, (b) –60 °C under 10 atm, (c) 15 °C under 56 atm?

 17

Answer the following questions based on the P – T phase diagram of CO2:

(a) CO2 at 1 atm pressure and temperature – 60 °C is compressed isothermally.


Does it go through a liquid phase?


(b) What happens when CO2 at 4 atm pressure is cooled from room temperature at constant pressure?


(c) Describe qualitatively the changes in a given mass of solid CO2 at 10 atm pressure and temperature –65 °C as it is heated up to room temperature at constant pressure.


(d) CO2 is heated to a temperature 70°C and compressed isothermally. What changes in its properties do you expect to observe?