What is Thermodynamic machine? — Physics

Definition 24.1 University Physics — Year 1 · Chapter 24 — Heat Engines and Machines

A thermodynamic machine is a closed system (the working fluid) taken round a cycle, so that it returns periodically to the same state, while exchanging work $W$ with the outside and heat $Q_i$ with sources at temperatures $T_i$ — thermostats, whose temperature the exchange does not change. A ditherm machine uses two thermostats, the hot source at $T_h$ and the cold source at $T_c < T_h$ . It is an engine if it delivers work ( $W < 0$ ), a refrigerator if it is driven ( $W > 0$ ) to take heat from the cold source, a heat pump if it is driven to give heat to the hot one. All quantities are reckoned over one cycle, algebraically, as received by the fluid.

The two ways round a ditherm cycle. Left: the engine takes heat from the hot source, rejects part of it to the cold one and delivers the difference as work. Right: the same machine driven backward pumps heat from cold to hot; it is a refrigerator if one wants Q_c, a heat pump if one wants |Q_h|. — The two ways round a ditherm cycle. Left: the engine takes heat from the hot source, rejects part of it to the cold one and delivers the difference as work. Right: the same machine driven backward pumps heat from cold to hot; it is a refrigerator if one wants $Q_c$ , a heat pump if one wants $|Q_h|$ .

Examples

Example 24.6 (Three numbers)

A steam turbine between $T_h = 800\,\mathrm{K}$ and a river at $T_c = 300\,\mathrm{K}$ : $\eta_C = 0.625$ ; real plants reach about $0.40$ . A domestic refrigerator between $275\,\mathrm{K}$ inside and a kitchen at $298\,\mathrm{K}$ : $e_f \leq 275/23 = 12$ ; real machines give $2$ to $4$ . A heat pump warming a house at $293\,\mathrm{K}$ from air at $273\,\mathrm{K}$ : $e_p \leq 293/20 = 14.7$ ; real pumps give $3$ to $5$ — still three to five times what the same electricity would give in a resistor (Problem 24.1).

Example 24.18 (Heat pump or resistor?)

A house losing $6\,\mathrm{kW}$ at $-5{}^{\circ}\mathrm{C}$ outdoors needs $6\,\mathrm{kW}$ of electricity with resistors; an ideal heat pump from $268\,\mathrm{K}$ to $293\,\mathrm{K}$ would need $6/11.7 = 0.51\,\mathrm{kW}$ ; a real one with exchanger temperatures $260\,\mathrm{K}$ and $313\,\mathrm{K}$ and a $0.55$ quality factor, $e_p = 0.55 \times 313/53 = 3.2$ , needs $1.9\,\mathrm{kW}$ . The weekend problem works the season through, entropy included.

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Examples

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