Num processo 20,9 J de calor são adicionados a 2,00 x 10^{-3} mol de um certo gás ideal. Como resultado, seu volume aumenta de 50,cm^3 para 100 cm^3, enquanto a pressão permanece constante em 2,00 x 10^5 Pa. A partir destas informações, pode-se afirmar que a variação na energia interna do gás neste processo e o calor específico molar à pressão constante desse certo gás ideal possuem os seguintes valores (Lembrete: R = 8,31 J/molK):

Let's break down the problem step by step. We are given that 20.9 J of heat is added to 2.00 × 10^-3 mol of an ideal gas, resulting in an increase in volume from 50 cm³ to 100 cm³, while the pressure remains constant at 2.00 × 10⁵ Pa.

We can use the ideal gas equation to relate the initial and final states of the system:

$PV = nRT$

Since the pressure is constant, we can write:

$Ptriangle V = nRtriangle T$

Substituting the given values, we get:

$2.00 times 10^5 Pa times 50 cm^3 = 2.00 times 10^{-3} mol times 8.31 J/molK times triangle T$

Solving for $triangle T$, we get:

$triangle T = 15.9 K$

Now, we can use the definition of specific heat capacity at constant pressure:

$C_p = frac{triangle Q}{ntriangle T}$

Substituting the given values, we get:

$C_p = frac{20.9 J}{2.00 times 10^{-3} mol times 15.9 K} = 34.7 J/molK$

Therefore, the correct answer is:

A) $triangle E_{int} = 15.9 J, C_p = 34.7 J/molK$

Explanation: We used the ideal gas equation and the definition of specific heat capacity at constant pressure to relate the given quantities and find the change in internal energy and the specific heat capacity of the ideal gas.