k B T + k B T + f k B T N A i.e., C v = ( + f ) R , C p = ( + f ) R , f f γ + = + ( . ) Note that C p – C v = R is true for any ideal gas, whether mono, di or polyatomic. Table . summarises the theoretical predictions for specific heats of gases ignoring any vibrational modes of motion.
The values are in good agreement with experimental values of specific heats of several gases given in Table . . Of course, there are discrepancies between predicted and actual values of specific heats of several other gases (not shown in the table), such as Cl , C H and many other polyatomic gases. Usually, the experimental values for specific heats of these gases are greater than the predicted values as given in Table12.
suggesting that the agreement can be improved by including vibrational modes of motion in the calculation. The law of equipartition of energy is, thus, well verified experimentally at ordinary temperatures. Table . Predicted values of specific heat capacities of gases (ignoring vibrational modes) Nature of Gas C v (J mol - K - ) C p (J mol - K - ) C p - C v (J mol - K - ) g Monatomic .
. . Table12. Measured values of specific heat capacities of some gases Example .
A cylinder of fixed capacity . litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by . ° C ?