To determine the heat capacity of the gas at constant volume, we can use the following equation:C_v = Q / T where C_v is the heat capacity at constant volume, Q is the change in energy absorbed by the gas, and T is the change in temperature.From the given data, we can calculate the average energy absorbed by the gas at each temperature increment. We can then use this information to find the heat capacity at constant volume.For example, let's say the energy absorbed by the gas at each increment is as follows:Q1 = 10 J, T1 = 2 KQ2 = 20 J, T2 = 4 KQ3 = 30 J, T3 = 6 KWe can calculate the heat capacity at constant volume for each increment:C_v1 = 10 J / 2 K = 5 J/KC_v2 = 20 J / 4 K = 5 J/KC_v3 = 30 J / 6 K = 5 J/KIn this example, the heat capacity at constant volume is the same for each increment, which is 5 J/K.Now, let's explain why the heat capacity at constant volume only depends on the temperature of the system. The heat capacity of an ideal gas at constant volume is given by the equation:C_v = n * c_vwhere n is the number of moles of the gas and c_v is the molar heat capacity at constant volume.For an ideal gas, the molar heat capacity at constant volume c_v is determined by the number of degrees of freedom f of the gas molecules. The relationship between c_v and f is given by the equation:c_v = f/2 * Rwhere R is the universal gas constant.For monatomic gases like argon, the number of degrees of freedom is 3 one for each spatial dimension: x, y, and z . Therefore, the molar heat capacity at constant volume for argon is:c_v = 3/2 * RSince the number of degrees of freedom and the universal gas constant are both constants, the molar heat capacity at constant volume for argon is also a constant. This means that the heat capacity at constant volume for argon only depends on the number of moles n and the temperature T of the system. In this case, the temperature determines the energy absorbed by the gas, which in turn determines the heat capacity at constant volume.