Final answer:
To find the change in the internal energy of the gas, we apply the first law of thermodynamics. The gas does 7.0 J of work while 31.4 J of heat is added, resulting in a change of 24.4 J in internal energy. Without additional information, the molar specific heat capacity cannot be calculated.
Step-by-step explanation:
The subject of the question is Physics, and the question would typically be encountered at the College level within the context of thermodynamics, a subfield that examines the relationships between heat, work, and energy.
Solution for the Question
To determine the change in the internal energy of the gas, we use the first law of thermodynamics, which is stated as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. Given that 31.4 J of heat is added (Q = 31.4 J) and the work done by the gas (W) can be calculated by the equation W = PΔV, where P is the pressure and ΔV is the change in volume. With a constant pressure of 1.40 × 104 Pa and a volume change from 3.00 × 10-4 m³ to 8.00 × 10-4 m³, the work done is:
W = (1.40 × 104 Pa) × (8.00 × 10-4 m³ - 3.00 × 10-4 m³) = 1.40 × 104 Pa × 5.00 × 10-4 m³ = 7.0 J
Now we can find the change in internal energy:
ΔU = Q - W = 31.4 J - 7.0 J = 24.4 J
For part (b), calculating the molar specific heat capacity requires additional information about the number of moles of gas or the type of gas to use the appropriate relation. Since the information provided is insufficient, we cannot calculate the molar specific heat capacity without additional data.