Chapter 4: Problem 7
Discuss the practical advantages and disadvantages of heat pumps and electric heating.
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Chapter 4: Problem 7
Discuss the practical advantages and disadvantages of heat pumps and electric heating.
These are the key concepts you need to understand to accurately answer the question.
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An engineer must design a refrigerator that does 300 J of work per cycle to extract \(2100 \mathrm{J}\) of heat per cycle from a freezer whose temperature is \(-10^{\circ} \mathrm{C}\). What is the maximum air temperature for which this condition can be met? Is this a reasonable condition to impose on the design?
Why don't we operate ocean liners by extracting heat from the ocean or operate airplanes by extracting heat from the atmosphere?
The temperature of the cold reservoir of the engine is 300 K. It has an efficiency of 0.30 and absorbs 500 J of heat per cycle. (a) How much work does it perform per cycle? (b) How much heat does it discharge per cycle?
(a) An infinitesimal amount of heat is added reversibly to a system. By combining the first and second laws, show that \(d U=T d S-d W\). (b) When heat is added to an ideal gas, its temperature and volume change from \(T_{1}\) and \(V_{1}\) to \(T_{2}\) and \(V_{2}\) Show that the entropy change of \(n\) moles of the gas is given by \(\Delta S=n C_{v} \ln \frac{T_{2}}{T_{1}}+n R \ln \frac{V_{2}}{V_{1}}\)
An ideal diesel cycle is shown below. This cycle consists of five strokes. In this case, only air is drawn into the chamber during the intake stroke \(O A\). The air is then compressed adiabatically from state \(A\) to state \(B\), raising its temperature high enough so that when fuel is added during the power stroke \(B C\), it ignites. After ignition ends at \(C\) there is a further adiabatic power stroke \(C D .\) Finally, there is an exhaust at constant volume as the pressure drops from \(p_{D}\) to \(p_{A}\) followed by a further exhaust when the piston compresses the chamber volume to zero. (a) Use \(W=Q_{1}-Q_{2}, \quad Q_{1}=n C_{p}\left(T_{C}-T_{B}\right), \quad\) and \(Q_{2}=n C_{v}\left(T_{D}-T_{A}\right)\) to show that \(e=\frac{W}{Q_{1}}=1-\frac{T_{D}-T_{A}}{\gamma\left(T_{C}-T_{B}\right)}\) (b) Use the fact that \(A \rightarrow B\) and \(C \rightarrow D\) are adiabatic to show that \(e=1-\frac{1}{\gamma} \frac{\left(\frac{V_{C}}{V_{D}}\right)^{\gamma}-\left(\frac{V_{B}}{V_{A}}\right)^{\gamma}}{\left(\frac{V_{C}}{V_{D}}\right)-\left(\frac{V_{B}}{V_{A}}\right)}\) (c) since there is no preignition (remember, the chamber does not contain any fuel during the compression), the compression ratio can be larger than that for a gasoline engine. Typically, \(V_{A} / V_{B}=15\) and \(V_{D} / V_{C}=5\) For these values and \(\gamma=1.4,\) show that \(e=0.56,\) or an efficiency of \(56 \%\). Diesel engines actually operate at an efficiency of about \(30 \%\) to \(35 \%\) compared with \(25 \%\) to \(30 \%\) for gasoline engines.
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