Q1: C_p/C_v for monoatomic gases is

ANS:B - 1.66

The ratio 𝐶𝑝𝐶𝑣Cv​Cp​​ for monoatomic gases is approximately 1.66. This value arises from the behavior of monoatomic gases, such as helium (He), neon (Ne), argon (Ar), and others, where the atoms within the gas molecules are not bonded to each other and do not have any internal degrees of freedom (such as rotation or vibration). The specific heat at constant volume (𝐶𝑣Cv​) represents the amount of heat required to raise the temperature of a unit mass of the gas by one degree Celsius at constant volume, while 𝐶𝑝Cp​ represents the amount of heat required to raise the temperature of the gas by one degree Celsius at constant pressure. For monoatomic gases, under typical conditions, most of the energy supplied to the gas is used to increase the translational kinetic energy of the atoms, resulting in an increase in temperature rather than any other form of energy (such as rotational or vibrational energy). As a result, the specific heat at constant volume (𝐶𝑣Cv​) primarily accounts for the increase in kinetic energy associated with the translation of the gas atoms. However, when the gas is heated at constant pressure (𝐶𝑝Cp​), in addition to the increase in kinetic energy associated with the translation of the gas atoms, some of the energy supplied is also used to do work against the external pressure, resulting in an increase in volume. This additional work done by the gas accounts for the higher value of 𝐶𝑝Cp​ compared to 𝐶𝑣Cv​. The ratio 𝐶𝑝𝐶𝑣Cv​Cp​​ for monoatomic gases, like helium or argon, is approximately 1.66, indicating that under normal conditions, slightly more heat is required to increase the temperature of the gas at constant pressure compared to constant volume. This value is a characteristic property of monoatomic gases and is derived from thermodynamic principles. For monoatomic gases, the ratio of specific heats (𝐶𝑝𝐶𝑣Cv​Cp​​) is approximately equal to 1.66. This value represents the ratio of the heat capacities at constant pressure (𝐶𝑝Cp​) and constant volume (𝐶𝑣Cv​) for monoatomic gases under normal conditions.