Question

Graph of specific heat at constant volume for a monatomic gas is:

A.

B.
 

C.
D.

 

Answer 1

Hint: Let us find the specific heat of a monatomic gas at constant volume. Also, we need to find the degrees of freedom of a monatomic gas, which is three. Therefore, the specific heat of a monatomic gas can be found. Lastly, we need to check how it is dependent on temperature.

Complete answer:
let us first find the formula of specific heat of any ideal gas at constant volume,
${{C}_{v}}=\dfrac{f}{2}R$
Here, f is the degrees of freedom and R is the universal gas constant.
For a monatomic gas, the value of f is three.
Therefore, the formula for specific heat of gas at constant volume is,
${{C}_{v}}=\dfrac{3}{2}R$
Therefore, it is clear that the formula of specific heat of monatomic gas at constant volume doesn’t depend on the temperature, clearing the correct option as option c.

Additional information:
The molar specific heat of a gas at constant pressure is the amount of heat required to raise the temperature of one mole of the gas by one degree at constant pressure. Similarly, specific heat of a gas at constant volume is the amount of heat required to raise the temperature of one mole on the gas by one degree at constant volume. In statistics, the number of degrees of freedom is the number of values in the final calculation of her statistics that are free to vary. The number of independent ways by which a dynamic system can move, without violating any constraints imposed on it East is called the number of degrees of freedom. The degrees of freedom for a monatomic gas is 3, the degrees of freedom for a diatomic gas is 5 and the degrees of freedom for polyatomic gas is 7.
Note:

Note:
As the formula of the specific heat of a monatomic gas at constant volume doesn’t depend on the temperature, the graph between the specific heat and the temperature will be constant, there won’t be any change and it results in a straight line.