I need help on physics hw...?

Question

1.('04B#12) An ideal gas may be taken from one state to another state with a different pressure, volume and temperature along several different paths. Quantities that will always be the same for this process, regradless of wich path is taken, include withc of the following?
I. the change in internal energy of the gas
II. the heat exchanged between the gas and its surroundings
III.the work done by the gas

2.('04B#57) A gas with a fixed number of molecules does 32 J of work on its surroundings and 16 J of heat are transferred from the gas to the surroundings. What happens to the internal energy of the gas?
a) it decreases by 48 J
b) it decreases by 16 J
c) It remains the same
d) it increases by 16 J
e) it increases by 48 J

3.('98B#24) In a certain process, 400J of heat is added to a system and the system simultaneously does 100J of work. The change in internal energy of the system is?

and if you can, i would like some explanations... thank you.

Answer 1

1.) To answer this question, examine each answer:
I.) A gas chanses state at the same energy threshold, no matter what the current pressure, volume, or temperature are. As long as the combined P, V, and T put the gas at the required energy threshold, the change in state will occur. Thus, this is your answer.
II.) If you change state by adding/removing heat (in other words, by changing temperature, ΔT), then heat is exchanged. However, you can also change the state by reducing the volume (which increases the pressure) and keeping heat constant. Since you can arrive at the change in state via many different levels of heat, this answer can't be right.
III.) This answer is the inverse of II. If you keep pressure and volume the same, and merely increase temperature, then the gas does no work. If you hold temperature constant, then the gas would do negative work, since you are doing work on the gas to decrease the pressure. Since the amount of work done is variable, this isn't the answer.

2.) Work and heat transfer are both forms of energy transfer. Thus, if I do 10 J of work on a box, I'm transferring 10 J of my energy to the box. So, since the gas transfers 16 J of heat, and does 32 J of work, it's transferring 48 J of its own energy to its surroundings - which decreases it's internal energy by 48 J (A.)

3.) Similar to #2. 400 J goes in as heat (positive ΔE), 100 J goes out as work (negative ΔE). +400 + -100 = +300 J internal energy.