Final answer:
The total change in the internal energy of the gas during the compression stroke is -422.8 Joules, calculated using the first law of thermodynamics and taking into account the work done on the surroundings and the heat lost to the surroundings.
Step-by-step explanation:
The total change in the internal energy of the gas during the compression stroke can be calculated using the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat transferred to the system (Q) minus the work done by the system (W). Since the gas is doing work on the surroundings and losing heat, both Q and W will be negative in this case. To find the work done by the gas, we can use the formula W = - PΔV, where P is the pressure and ΔV is the change in volume. Using the given values, the initial volume (Vi) is 400 mL, the final volume (Vf) is 50 mL, and the pressure is 8.0 atm. The volume change ΔV is Vf - Vi = -350 mL or -0.35 L since 1 L = 1000 mL. The work done by the gas is W = -8.0 atm × -0.35 L. To convert this into Joules, we use the conversion factor 1 L atm = 101.3 J, so the work done is W = 8.0 atm × 0.35 L × 101.3 J/L atm = 282.8 J.
The heat transferred from the gas is given as Q = -140 J (since it's being transferred from the gas to the surroundings). Therefore, the total change in the internal energy of the gas is ΔU = Q - W = -140 J - 282.8 J = -422.8 J. This indicates the gas's internal energy has decreased by 422.8 Joules during the compression.