Physics homework help on thermodynamics

Question

Part 1) Two moles of helium gas initially at 148 K and 0.47 atm are compressed isothermally to 1.27 atm.

Find the final volume of the gas. Assume that helium behaves as an ideal gas. The universal gas constant is 8.31451 J/K · mol.

Answer in units of m3.

Part 2) Find the work done by the gas. Answer in units of kJ.

Part 3) Find the thermal energy transferred. Answer in units of kJ.

Answer 1

Hi Emma, I hope I'm not too late to help.

For Part 1: Knowing the final pressure, number of moles, and that the gas was compressed isothermally (no change in temperature) you can get the answer by using PV=nRT. But be aware that the pressure unit of atmospheres isn't in SI so you'll want to convert to Pascals (1 atm ≈ 101 kPa)

Having all of that you can plug in the values to the bolded equation above to get

(47470 Pa) V₂ = (2 mol) (8.31451 J/K·mol) (148 K)

I got: V₂ = 0.019 m³

For Part 2: The second part is also a lot of plugging and chugging into an equation but that needs to get set up first. For any isothermal ideal gas, the value of pressure times volume is going to be constant. From the equation above, we can always see that PV is equal to the number of moles, temperature, and gas constant. How this plays into calculating the work is the equation

W_A→B = ∫ P dV

Knowing that PV is constant, the integral simplifies to

W = nRT ln(V_B / V_A)

Now you can just plug in your value from Part 1 for V_B and use the same strategy from Part 1 to get V_A

W = (2 mol) (8.31451 J/K·mol) (148 K) ln(0.019 m³ / 0.052 m³)

I got: W = -2.478 kJ

For Part 3: An isothermal process simplifies the first law of thermodynamics to

ΔU = Q - W = 0

Where W is the work we just found, Q is the heat transfer, and U is the internal energy

Since the change in internal energy must be zero you can find Q to be -2.478 kJ as well.

I hope this all helps, let me know if I can clarify anything further!