**Specific Heat at Constant Volume**

The specific heat at constant volume, denoted as Cv, is a thermodynamic property that represents the amount of heat energy required to raise the temperature of a substance by 1 unit when the volume remains constant. In order to determine the specific heat at constant volume for the given gas equation (T^(7/5) / P^(2/5)), we need to consider the definition of specific heat and the properties of the gas.

**Definition of Specific Heat at Constant Volume**

The specific heat at constant volume (Cv) is defined as the ratio of the change in internal energy (∆U) of a system to the corresponding change in temperature (∆T), while keeping the volume constant:

Cv = ∆U / ∆T

**Properties of the Given Gas Equation**

The given gas equation is T^(7/5) / P^(2/5). Let's break it down to understand the properties of the equation:

- T represents temperature
- P represents pressure

**Calculating ∆U and ∆T**

To calculate ∆U and ∆T, we need to consider a change in temperature (∆T) while keeping the volume constant. Let's assume that the initial temperature is T1 and the final temperature is T2.

∆T = T2 - T1

**Calculating ∆U**

To calculate ∆U, we need to integrate the given gas equation with respect to temperature (T) while keeping the volume constant:

∆U = ∫[T1, T2] (T^(7/5) / P^(2/5)) dT

Integrating the equation will give us the change in internal energy (∆U) for the given temperature range.

**Calculating Specific Heat (Cv)**

Once we have the values of ∆U and ∆T, we can calculate the specific heat at constant volume (Cv) using the formula:

Cv = ∆U / ∆T

Substituting the values of ∆U and ∆T into the formula will give us the specific heat at constant volume for the given gas equation.

Note: The specific heat at constant volume for the given gas equation cannot be determined without additional information, such as the range of temperatures or specific values for T1 and T2.