See u have to simply apply TV raised power gamma-1. now raised power is 0.4 that means gamma -1 is equal to 0.4. now we have gamma as 1.4.now see we have gamma =7/5(1.4) for diatomic gases. so its a diatomic gas i.e. hydrogen. hope so my answer is correct.

Answer:

The given relation between temperature and volume for a gas undergoing an adiabatic process is TV^0.4 = constant. Based on this relation, it can be concluded that the gas is hydrogen.

Explanation:

To understand why the gas must be hydrogen, let's break down the information provided.

Adiabatic Process:
An adiabatic process is a thermodynamic process in which there is no exchange of heat between the system and its surroundings. In other words, the process occurs without any heat transfer.

Relation between Temperature and Volume:
The given relation between temperature (T) and volume (V) is TV^0.4 = constant. This implies that the product of temperature and volume raised to the power of 0.4 remains constant throughout the adiabatic process.

Identifying the Gas:
To determine the gas involved in this adiabatic process, we can examine the ideal gas law, which states:

PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature

For an adiabatic process, the ideal gas law can be written as:

PV^(γ) = constant

Where γ is the ratio of specific heat capacities (Cp/Cv) for the gas.

For monoatomic gases like helium and hydrogen, the value of γ is approximately 5/3. However, for diatomic gases like oxygen and nitrogen, the value of γ is approximately 7/5.

Relation between γ and the given relation:
In the given relation TV^0.4 = constant, the exponent of V is 0.4. To find the value of γ, we can equate the exponent of V to γ:

0.4 = γ

Since the value of γ for monoatomic gases is approximately 5/3, it can be concluded that the gas involved in the adiabatic process is hydrogen.

Conclusion:
Based on the given relation between temperature and volume in an adiabatic process, TV^0.4 = constant, the gas involved is hydrogen. This conclusion is supported by the value of γ for hydrogen, which corresponds to the exponent of volume in the given relation.