Assertion (A) : The ratio of specific heat of a gas at constant pressure and specific heat at constant volume for a diatomic gas is more than that for a monatomic gas.Reason (R) : The molecules of a monatomic gas have more degree of freedom than those of a diatomic gas.

Step 1: Understand the assertion and reason given in the question.

The assertion states that the ratio of specific heat at constant pressure to specific heat at constant volume is higher for a diatomic gas compared to a monatomic gas.

The reason provided is that the molecules of a monatomic gas have more degrees of freedom than those of a diatomic gas.

Step 2: Analyze the assertion and reason.

The specific heat of a gas is a measure of how much heat energy is required to raise the temperature of the gas. The specific heat at constant pressure (Cp) is the amount of heat required to raise the temperature of the gas while keeping the pressure constant. The specific heat at constant volume (Cv) is the amount of heat required to raise the temperature of the gas while keeping the volume constant.

For a diatomic gas, the molecules consist of two atoms bonded together. These molecules have additional degrees of freedom compared to monatomic gases, which have only one atom per molecule. Degrees of freedom refer to the number of independent ways a molecule can store energy, such as translational, rotational, and vibrational motion.

Step 3: Evaluate the assertion and reason.

The assertion states that the ratio of Cp to Cv is higher for a diatomic gas compared to a monatomic gas. This is because diatomic gases have additional degrees of freedom due to the presence of two atoms in each molecule. These additional degrees of freedom allow diatomic gases to store more energy, resulting in a higher Cp value.

The reason provided supports the assertion by explaining that monatomic gases have fewer degrees of freedom compared to diatomic gases. Since monatomic gases have only one atom per molecule, they have fewer ways to store energy, resulting in a lower Cp value.

Step 4: Draw a conclusion.

Based on the analysis, we can conclude that the assertion is true and the reason is a valid explanation for the assertion. The ratio of specific heat at constant pressure to specific heat at constant volume is indeed higher for a diatomic gas compared to a monatomic gas due to the difference in degrees of freedom.