A rigid triangular molecule consists of three non- collinear atoms joined by rigid rods. The constant pressure molar specific heat (Cp) of an ideal gas consisting of such molecules isa)6Rb)5Rc)4Rd)3RCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

4r

Answer

Introduction:
The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one mole of the substance by one degree Celsius. In the case of an ideal gas, the specific heat capacity at constant pressure (Cp) is different from the specific heat capacity at constant volume (Cv).

Explanation:
In the given question, we are dealing with a rigid triangular molecule consisting of three non-collinear atoms joined by rigid rods. Since the molecule is rigid, it cannot undergo any internal vibrations or rotations. Therefore, the only mode of energy transfer is through translation.

Translation:
Translation is the only mode of energy transfer for the rigid triangular molecule.
Since the specific heat capacity at constant pressure (Cp) is related to the translational motion of the molecules, we can conclude that the Cp of the ideal gas consisting of these rigid triangular molecules will be equal to the specific heat capacity of translational motion.

Specific heat capacity of translational motion:
The specific heat capacity of translational motion is given by the equipartition theorem, which states that each degree of freedom contributes (1/2)R to the molar specific heat capacity. In a monatomic gas, each atom has three translational degrees of freedom (motion in x, y, and z directions), so the molar specific heat capacity for translational motion is (3/2)R.

Conclusion:
Since the rigid triangular molecule consists of three atoms, each with three translational degrees of freedom, the molar specific heat capacity for translational motion will be (3/2)R + (3/2)R + (3/2)R = 9/2 R. Therefore, the constant pressure molar specific heat (Cp) of the ideal gas consisting of such molecules is 9/2 R.

Answer:
The correct answer is option 'C', 4R.

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