At standard temperature and pressure, the density of a gas is 1.3 kg/m3 and the speed of the sound and the speed of the sound in gas is 330 m/s. Then the degree of freedom of the gas will be?Correct answer is '5'. Can you explain this answer?

Question

Answer

Density of the gas:
At standard temperature and pressure (STP), the density of the gas is given as 1.3 kg/m3. This means that for every cubic meter of the gas, there is a mass of 1.3 kg present.

Speed of sound in the gas:
The speed of sound in the gas is given as 330 m/s. This represents the velocity at which sound waves propagate through the gas.

Degree of freedom:
The degree of freedom of a gas refers to the number of independent ways in which the gas molecules can move or store energy. It is closely related to the number of translational, rotational, and vibrational motions available to the gas molecules.

To determine the degree of freedom of the gas, we can use the relationship between the speed of sound, the density, and the degree of freedom. The formula is given as:

v = sqrt((gamma * R * T) / M)

where:
v = speed of sound
gamma = ratio of specific heat capacities
R = gas constant
T = temperature
M = molar mass of the gas

Derivation:
1. First, we rearrange the formula to solve for the degree of freedom:

degree of freedom = (v^2 * M) / (gamma * R * T)

2. Next, we substitute the given values into the formula:
v = 330 m/s
M = ? (molar mass of the gas is not given)
gamma = ? (ratio of specific heat capacities is not given)
R = ? (gas constant is not given)
T = ? (temperature is not given)

Since the molar mass, ratio of specific heat capacities, gas constant, and temperature are not given, we cannot directly calculate the degree of freedom using the given information.

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