An inventor claims to have built a heat engine that absorbs 1000 J from a hot reservoir and converts exactly 1000 J into useful work, rejecting nothing to a cold reservoir. Which law of physics does this violate?
AThe First Law of Thermodynamics — energy is not conserved if nothing is rejected
BThe Second Law of Thermodynamics — complete conversion of heat to work is forbidden even when energy is conserved
CBoth the First and Second Laws — such a device is doubly impossible
DNeither law, in principle — this would require only a perfectly frictionless engine
The First Law is satisfied: 1000 J in, 1000 J out as work, 0 J rejected — energy is conserved. The violation is of the Second Law, which forbids any engine from converting heat entirely into work in a cyclic process. Such a device would be a perpetual motion machine of the second kind. The Second Law is about direction and quality of energy, not quantity — heat cannot be fully upgraded to work without rejecting some to a cold reservoir, regardless of engineering perfection.
Question 2 Multiple Choice
A heat engine absorbs Q_H = 800 J from its hot reservoir in one cycle and does W = 300 J of mechanical work. How much heat Q_C is rejected to the cold reservoir?
A300 J — the rejected heat equals the work output
B500 J — the rejected heat equals Q_H minus W
C800 J — all the absorbed heat must eventually be rejected to maintain the cycle
DIt cannot be determined without knowing the temperatures of the reservoirs
For a complete cycle, ΔU = 0 (the working substance returns to its initial state). The first law gives W = Q_H − Q_C, so Q_C = Q_H − W = 800 − 300 = 500 J. The energy flow is: 800 J in from the hot reservoir, 300 J out as work, 500 J out to the cold reservoir. These three quantities always satisfy Q_H = W + Q_C. The temperature information determines maximum efficiency but not the energy balance, which follows from the first law alone.
Question 3 True / False
For a heat engine operating in a complete thermodynamic cycle, the change in internal energy of the working substance over one full cycle is zero.
TTrue
FFalse
Answer: True
This is the key property of a cyclic process: after one complete cycle, the working substance (steam, gas, etc.) returns to exactly its original thermodynamic state — same temperature, pressure, and volume. Internal energy is a state function, so ΔU = 0 for any process that returns to the starting state. This is what allows the First Law to simplify to W = Q_H − Q_C for a full cycle, making the energy accounting straightforward.
Question 4 True / False
A sufficiently well-engineered heat engine — one with perfectly smooth bearings, no friction losses, and ideal gas behavior — could in principle achieve 100% thermal efficiency.
TTrue
FFalse
Answer: False
100% efficiency requires Q_C = 0: all absorbed heat converted to work with nothing rejected. The Second Law of Thermodynamics forbids this regardless of engineering quality. It is not a matter of friction or practical limitations — a completely frictionless, ideal engine still must reject heat to a cold reservoir. The fundamental reason is that heat naturally flows from hot to cold, and completely reversing this direction for all the energy in the system is thermodynamically prohibited. The Carnot efficiency 1 − T_C/T_H gives the absolute maximum, which is always less than 1 whenever T_C > 0 K.
Question 5 Short Answer
A heat engine operates between two reservoirs with no friction and ideal thermodynamic processes. Explain why it still cannot convert all absorbed heat into work — what fundamental principle prevents 100% efficiency?
Think about your answer, then reveal below.
Model answer: The Second Law of Thermodynamics requires that any cyclic process transferring energy from a hot reservoir must reject some heat to a cold reservoir. A complete conversion would require entropy to decrease in the universe — which the Second Law forbids. Equivalently, such a device would be a perpetual motion machine of the second kind: it would spontaneously convert disordered thermal energy (heat) entirely into ordered mechanical energy (work) without any compensating change elsewhere. The direction of heat flow — always from hot to cold — is itself the Second Law's content, and no engineering improvement can circumvent it.
This is fundamentally different from the First Law. The First Law (energy conservation) is satisfied by a 100%-efficient engine: energy in = energy out. The Second Law adds a constraint on the direction and quality of that energy transformation. The Carnot efficiency 1 − T_C/T_H shows that efficiency approaches 1 only as T_C → 0 K (absolute zero) or T_H → ∞, neither of which is physically achievable. Real engines fall short even of this theoretical maximum due to irreversibilities.