Question
A process stream is heated as a gas from 298.15 to $523.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right.$ to $\left.250^{\circ} \mathrm{C}\right)$ at constant pressure. A quick estimate of the energy requirement is obtained from Eq. (4.3), with $C_P$ taken as constant and equal to its value at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Is the estimate of $\mathrm{Q}$ likely to be low or high? Why?
Step 1
15 K and the final temperature is 523.15 K, the change in temperature is $\Delta T = 523.15 \, \text{K} - 298.15 \, \text{K} = 225 \, \text{K}$. Show more…
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A process stream is heated as a gas from 298.15 to $523.15 \mathrm{K}\left(25^{\circ} \mathrm{C} \text { to } 250^{\circ} \mathrm{C}\right)$ at constant pressure. A quick estimate of the energy requirement is obtained from Eq. (4.3), with $C_{P}$ taken as constant and equal to its value at $298.15 \mathrm{K}\left(25^{\circ} \mathrm{C}\right) .$ Is the estimate of $\mathrm{Q}$ likely to be low or high? Why?
Carbon dioxide gas is heated as it flows steadily through a 2.5-cm-diameter pipe. At the inlet, the pressure is 2 bar, the temperature is $300 \mathrm{~K}$, and the velocity is $100 \mathrm{~m} / \mathrm{s}$. At the exit, the pressure and velocity are $0.9413$ bar and $400 \mathrm{~m} / \mathrm{s}$, respectively. The gas can be treated as an ideal gas with constant specific heat $c_{p}=0.94 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$. Neglecting potential energy effects, determine the rate of heat transfer to the carbon dioxide, in $\mathrm{kW}$.
Control Volume Analysis Using Energy
Problems: Developing Engineering Skills
An ideal gas undergoes a reversible, steady-flow process in which pressure and volume are related by the polytropic equation $P v^{n}=$ constant. Neglecting the changes in kinetic and potential energies of the flow and assuming constant specific heats, $(a)$ obtain the expression for the heat transfer per unit mass flow for the process and ( $b$ ) evaluate this expression for the special case where $n=k=c_{p} / c_{v}$.
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