godstimeprince511
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1m of air initially at 110kn/m^2 and 15°c, is compressed according to the law if pv^1.3=constant in a cylinder to final pressure of 1.4mn/m^2, taking R for air = 287j/kgk and cp=1005j/kgk, determine
the volume and temperature of the air at the end of the compression
the work done in compressing the air
the change of internal energy
the heart exchange through the cylinder walls stating the direction of heat flow.
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Respuesta :

[tex]$\begin{aligned} (a) &=1 m^{3} \\ V_{1} &=110 \times 10^{3} \mathrm{~Pa} \\ T_{1} &=15+273=288 \mathrm{~K} \end{aligned}$[/tex]

[tex]$c_{p}=1005 \frac{\mathrm{J}}{\mathrm{kg} K}$[/tex]

[tex]$P_{2}=1400 \times 10^{3} \mathrm{~Pa}$[/tex]

[tex](i)$P_{1} V_{1}^{1 / 3}=P_{2} V_{2}^{1 / 3}$[/tex]

[tex]$\Rightarrow \quad\left(\frac{110}{1400}\right)=\left(\frac{V_{2}}{1}\right)^{\$ 1 \cdot 3} \Rightarrow V_{2}=A \cdot 85 \times 10^{4} / \ln ^{3}$[/tex]

[tex]$\Rightarrow \quad V_{2}=0.1413 \mathrm{~m}^{3}$[/tex]

[tex]$T_{2}=T_{1}\left(\frac{p_{2}}{p_{1}}\right)^{\frac{1 \cdot 3 \cdot 1}{1 \cdot 3}}=$[/tex] [tex]$288\left(\frac{1400}{110}\right)^{\frac{1 \cdot 3-1}{1 \cdot 3}}=518 \mathrm{~K}$[/tex]

[tex](ii) $W=\frac{P_{1} v_{1}-P_{2} V_{2}}{n-1}=\frac{\left(110 \times 10^{3} \times 1\right)-\left(1400 \times 10^{3}\right)(0.1413)}{1.3-1}$[/tex]

[tex]$\Rightarrow W=-292.73 \mathrm{~kJ}$[/tex]

[tex](iii) $\quad \Delta U=m C_{V} \Delta T$[/tex]

[tex]$=\frac{p_{1} V_{1}}{p_{1}}\left( R-C_{p}\right) \times\left(T_{2}-T_{1}\right)$[/tex]

[tex]$=\frac{110 \times 10^{3} \times 1(-287+1005)(518-288)}{287 \times 288}$[/tex]

[tex]$\Delta U=219.77 \mathrm{~kJ}$[/tex]

[tex](iv)$Q-W=\Delta U$[/tex]

[tex]$\Rightarrow Q-(-292.73)=219.7 7$[/tex]

[tex]$\Rightarrow Q=-72.96 \mathrm{~kJ}$[/tex]

[tex]$\rightarrow$[/tex] Heat is flowing form surrounding

(b) Since, Tempererature is contant So, change in Internal energy [tex]$\Rightarrow \Delta U=m C_{v} \Delta T^{\circ} \Rightarrow \Delta U=0$[/tex]

What is Internal energy ?

  • Internal energy, which emerges from the molecular state of motion of matter, is an energy form inherent in all systems. Internal energy is represented by the symbol U, and the unit of measurement is the joule (J).
  • Internal energy increases when temperature rises and states or phases transition from solid to liquid and liquid to gas. Planetary bodies can be viewed as hybrids of heat reservoirs and heat engines.
  • Internal energy E is stored in the heat reservoirs, and heat engines transform some of this thermal energy into mechanical, electrical, and chemical energies.

Learn more about Internal energy https://brainly.com/question/11278589

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