[tex]\displaystyle{ \nu = 1 \ mol }[/tex]
[tex]\displaystyle{ monoatomic \rightarrow C_{V} = \frac{3}{2} R }[/tex]
[tex]\displaystyle{ V_{1} = 16,62 \ l = 2 \cdot 8,31 \ l = 2 \cdot 8,31 \cdot 10^{-3} \ m^{3} }[/tex]
[tex]\displaystyle{ p_{1} = 4 \cdot 10^{5} \ Pa }[/tex]
[tex]\displaystyle{ trans. \ izocora \rightarrow \nu = constant, \ V = constant \rightarrow V_{1} = V_{2} = V }[/tex]
[tex]\displaystyle{ p_{2} = p_{1} + 15\% = 115\% \cdot p_{1} }[/tex]
[tex]\displaystyle{ p_{2} = \frac{115 \cdot 4 \cdot 10^{5}}{100} = 4,6 \cdot 10^{5} \ Pa }[/tex]
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[tex]\displaystyle{ a) \ T_{1} = ? }[/tex]
[tex]\displaystyle{ b) \ T_{2} = ? }[/tex]
[tex]\displaystyle{ c) \ Q, L, \Delta U = ? }[/tex]
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a) [tex]\displaystyle{ p_{1} \cdot V = \nu \cdot R \cdot T_{1} }[/tex]
[tex]\displaystyle{ T_{1} = \frac{p_{1} \cdot V}{\nu \cdot R} = \frac{4 \cdot 10^{5} \cdot 2 \cdot 8,31 \cdot 10^{-3}}{1 \cdot 8,31} }[/tex]
[tex]\displaystyle{ T_{1} = 8 \cdot 10^{2} = 800 \ K }[/tex]
b) [tex]\displaystyle{ p_{2} \cdot V = \nu \cdot R \cdot T_{2} }[/tex]
[tex]\displaystyle{ T_{2} = \frac{p_{2} \cdot V}{\nu \cdot R} = \frac{4,6 \cdot 10^{5} \cdot 2 \cdot 8,31 \cdot 10^{-3}}{1 \cdot 8,31} }[/tex]
[tex]\displaystyle{ T_{2} = 4,6 \cdot 2 \cdot 10^{2} = 920 \ K }[/tex]
c) L = 0
[tex]\displaystyle{ Q = \Delta U = \nu \cdot C_{V} \cdot \Delta T }[/tex]
[tex]\displaystyle{ Q = \Delta U = \nu \cdot \frac{3}{2} R \cdot (T_{2} - T_{1}) }[/tex]
[tex]\displaystyle{ Q = \Delta U = \frac{3}{2} \cdot (p_{2}V - p_{1}V) }[/tex]
[tex]\displaystyle{ Q = \Delta U = \frac{3}{2} \cdot V \cdot (p_{2} - p_{1}) }[/tex]
[tex]\displaystyle{ Q = \Delta U = \frac{3}{2} \cdot 2 \cdot 8,31 \cdot 10^{-3} \cdot (4,6 \cdot 10^{5} - 4 \cdot 10^{5}) }[/tex]
[tex]\displaystyle{ Q = \Delta U = 3 \cdot 8,31 \cdot 10^{-3} \cdot 0,6 \cdot 10^{5} }[/tex]
[tex]\displaystyle{ Q = \Delta U = 1,8 \cdot 8,31 \cdot 10^{2} }[/tex]
[tex]\displaystyle{ Q = \Delta U = 180 \cdot 8,31 }[/tex]
Q = ΔU = 1495,8 J
Matei.
