For a monatomic gas, the molar specific heat at constant volume is \(C_V = \frac{3}{2}R\), and for a diatomic gas, \(C_V = \frac{5}{2}R\). The total heat capacity \(C_V\) of the mixture is given by the weighted average formula:
\[ C_V = \frac{n_1C_{V1} + n_2C_{V2}}{n_1 + n_2} \]
Where:
Substituting the values into the equation:
\[ C_V = \frac{2 \times \frac{3}{2}R + 6 \times \frac{5}{2}R}{2 + 6} = \frac{3R + 15R}{8} = \frac{18R}{8} = \frac{9}{4}R \]
Thus, the molar specific heat of the mixture at constant volume is \(\frac{9}{4}R\).
List-I | List-II | ||
P | The value of \(I1\) in Ampere is | I | \(0\) |
Q | The value of I2 in Ampere is | II | \(2\) |
R | The value of \(\omega_0\) in kilo-radians/s is | III | \(4\) |
S | The value of \(V_0\) in Volt is | IV | \(20\) |
200 |
The pressure of a gas changes linearly with volume from $A$ to $B$ as shown in figure If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be Is