One mole of an ideal gas undergoes a process described by p = p₀ 1 + (V/V₀)^2 , where p₀ and V₀ represent constants. Determine the temperature of the gas when V = V₀ .

Step-by-step solution

The equation of the process is given by p = p₀ 1 + (V/V₀)^2 . Substituting V = V₀ into the given equation: p = p₀ 1 + (V₀/V₀)^2 = p₀ 1 + 1 = p₀ 2 For one mole of an ideal gas, the ideal gas equation is pV = RT . Substituting the values of p and V at this state: ( p₀ 2 ) V₀ = RT T = p₀ V₀ 2R