Final answer:
The change in internal energy of the gas when it is compressed adiabatically to half its volume, with 2650 J of work done on it, is an increase of 2650 J.
Step-by-step explanation:
The question pertains to a scenario in an engine where an almost ideal gas is compressed adiabatically to half its volume, and 2650 J of work is done on the gas. When a gas is compressed adiabatically, there is no heat exchange with the surroundings (Q=0). According to 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), we can find the change in internal energy for this process. In mathematical form, it is ΔU = Q - W.
However, since the process is adiabatic, Q = 0 J, which simplifies the equation to ΔU = -W. When work is done on the gas, W is positive; therefore, ΔU = -2650 J. This indicates that the internal energy of the gas increases by 2650 J as the gas is compressed.