With what minimum pressure (in MPa) must a given volume of nitrogen gas ( C v , m = 5/2 R ) , originally at 300K and 0.10 MPa pressure, be adiabatically compressed in order to raise its temperature

Question

With what minimum pressure (in MPa) must a given volume of nitrogen gas ( C v , m ​ = 5/2 R ) , originally at 300K and 0.10 MPa pressure, be adiabatically compressed in order to raise its temperature to 600K.

TestHub · Accepted Answer

For minimum pressure, the process should be irreversible. Now,

$Δ U = w$

$n \cdot C_{v, m} \cdot (T_{2} - T_{1}) = - P_{e x t} (V_{2} - V_{1})$

$n \frac{5}{2} R \cdot (600 - 300) = - P_{2} (\frac{n R \cdot 600}{P _{2}} - \frac{n R \cdot 300}{P _{1}})$

$\Rightarrow P_{2} = 0.45 MP a$

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