Explain why? 1) 500 joules of …

In thermodynamics, the first law (which is essentially the law of conservation of energy) states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on the surroundings. Mathematically, it is written as: ΔU = Q - W - ΔU is the change in internal energy of the system. - Q is the heat added to the system. - W is the work done by the system on its surroundings. For an adiabatic process, no heat is exchanged with the surroundings, which means Q = 0. Therefore, the equation simplifies to: ΔU = -W However, in this case, you are compressing the gas, meaning you are doing work on the gas, not the other way around. The sign convention for work in thermodynamics can be a bit counterintuitive: work done on the system is considered positive, and work done by the system is negative. Therefore, the work you've done on the gas, 500 joules, is positive from the perspective of the gas. So, for the gas being compressed adiabatically: W (on the gas) = 500 joules Therefore, the change in internal energy (ΔU) will be equal in magnitude but positive, since no heat is being added or removed: ΔU = 500 joules Thus, the internal energy of the gas increases by 500 joules. This increase in internal energy can result in an increase in temperature of the gas since the energy is not being used to do work by the gas or being lost as heat to the surroundings.