Correct Answer - Option 1 : Molar heat capacity at constant volume,
\(C_v = \dfrac{3}{2} R\)
CONCEPT:
- The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.
\({C_v} = {\left( {\frac{\Delta Q}{{n\Delta T}}} \right)_{constant\;volume}}\)
- The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.
\({C_p} = {\left( {\frac{{\Delta Q}}{{n\Delta T}}} \right)_{constant\;pressure}}\)
Monatomic Gas:
- A monatomic gas is one in which atoms are not bound to each other.
-
Monatomic gas consists of single atoms.
- Example: argon, krypton, and xenon.
EXPLANATION:
- For a monoatomic gas, the molar heat capacity at constant volume is given as,
\(⇒ C_v = \dfrac{3}{2} R\)
- Hence, option 1 is correct.
- For a monoatomic gas, the molar heat capacity at constant pressure is given as,
\(⇒ C_P = \dfrac{5}{2} R\)
- For a monoatomic gas, the ratio of Cp and Cv is,
\(⇒ \frac{C_{p}}{C_{v}}=\frac{5}{2}\times\frac{2}{3}\)
\(⇒ \frac{C_{p}}{C_{v}}=\frac{5}{3}\)
\(⇒ \frac{C_{p}}{C_{v}}=1.67\)
The difference between Cp and Cv is given by Mayer's formula,
⇒ Cp - Cv = R
