Q4. A system does 50 J of work on its surroundings and its internal energy falls by 80 J. How much heat did it gain or lose?
w = −50 J and ΔU = −80 J, so q = ΔU − w = −80 − (−50) = −30 J: the system lost 30 J of heat.
Q5. A reaction in a sealed, rigid, insulated flask releases energy and the contents warm from 25 °C to 40 °C. Has the system’s internal energy changed?
No. q = 0 and w = 0, so ΔU = 0; chemical energy has become thermal energy inside the system.
Q6. A physics book writes the first law as ΔU = Q − W. For a gas that absorbs 500 J of heat and does 200 J of work in expanding, show that both conventions give the same ΔU.
Physics: Q = 500 J, W = 200 J (work done by the gas), ΔU = 500 − 200 = 300 J. Chemistry: q = +500 J, w = −200 J (work done by the system is negative), ΔU = 500 + (−200) = 300 J. Same answer.
Q7. Is a living cell an open, closed or isolated system? Give a reason.
Open: it exchanges nutrients and wastes across its membrane (aerobic cells also take up oxygen and release carbon dioxide), and it exchanges heat with its surroundings.
Q8. Water in an insulated flask is taken from state A to state B by 1 kJ of paddle work. The same change A → B is then made in a rigid copper vessel by heating alone. How much heat does the water absorb, and what is ΔU each time?
ΔU depends only on A and B: ΔU = wad = +1 kJ both times. In the second route w = 0, so q = +1 kJ.