Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
At ordinary temperatures, the molecules of an ideal gas have only translational and rotational kinetic energies. At high temperatures they may also have vibrational energy. As a result of this at higher temperatures (\[{{C}_{v}}=\]molar heat capacity at constant volume) (1)\[{{C}_{V}}=\frac{3}{2}R\]fora monoatomic gas (2)\[{{C}_{V}}=\frac{3}{2}R\]for a monoatomic gas (3)\[{{C}_{V}}>\frac{5}{2}R\]for a diatomic gas (4)\[{{C}_{V}}>\frac{5}{2}R\] for a diatomic gasA) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: D
Solution :
Vibrational kinetic energy of a monoatomic gas\[=0\]at all temperatures. So, \[{{C}_{V}}=\frac{3}{2}R\]for a monoatomic gas even at high temperatures also. In case of a diatomic gas\[{{C}_{V}}=\frac{5}{2}R\]at low temperatures, while\[{{C}_{V}}>\frac{5}{2}R\]at high temperatures due to vibrational kinetic energy.
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