Please someone help me out I'm so confused!

A system consists of 2.0mol of an ideal monatomic gas at 375 K . How much heat must be added to the system to double its internal energy (a)at constant pressure or (b)at constant volume.

To find the amount of heat needed to double the internal energy of a system, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W).

(a) In the case of constant pressure, we have to consider the heat added at constant pressure, which is also known as enthalpy change (ΔH). The equation relating the enthalpy change to the heat added is given by ΔH = Qp, where Qp is the heat added at constant pressure.

To find ΔH, we can use the equation ΔH = nCpΔT, where n is the number of moles of gas, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature.

In this case, ΔU = Q - W, but since the system is at constant pressure, the work done W = PΔV, where P is the pressure and ΔV is the change in volume. However, in this case, we are interested in the change in internal energy, so W = PΔV = ΔH - Q. Rearranging the equation, we get Q = ΔH - ΔU.

Substituting the values given:
n = 2.0 mol
Cp (for monatomic gas) = 5/2 R, where R is the ideal gas constant (8.314 J/(mol·K))
ΔT = 375 K

We can calculate ΔH using the equation ΔH = nCpΔT, and then find Q using Q = ΔH - ΔU, where ΔU is twice the initial internal energy of the system.

(b) In the case of constant volume, no work is done by the system (W = 0), and the equation becomes ΔU = Qv, where Qv is the heat added at constant volume.

Again, we will use the equation ΔU = Q - W, but since W = 0, we have Q = ΔU.

By substituting the values given:
n = 2.0 mol
Cv (for monatomic gas) = 3/2 R
ΔT = 375 K

We can calculate Q directly using the equation Q = ΔU, where ΔU is twice the initial internal energy of the system.

Remember to convert temperature to Kelvin if necessary and ensure the units are consistent.

Now you should be able to calculate the amount of heat required using the given equations and values provided.