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One cubic meter of nitrogen at 40Ā°C and 340kPa is compressed isoentropically to 0.2m^3. Calculate the final pressure when the nitrogen is reduced to that volume. What is the modulus of elasticity at the beginning and end of the compression? (k = 1.4)

Respuesta :

Answer:

a)Pā‚‚=3236.21 KPa

b)E=3620.26 KPa

Explanation:

Given that

Vā‚= 1 mĀ³

Tā‚=40Ā°C

Pā‚= 340 KPa

Vā‚‚=0.2 mĀ³

k= 1.4

We know that for Ā isentropic process

[tex]PV^{k}=C[/tex]

[tex]P_1V_1^{k}=P_2V_2^{k}[/tex]

[tex]340\times 1^{1.4}=P_2\times 0.2^{1.4}[/tex]

Pā‚‚=3236.21 KPa

Final pressure of gas Pā‚‚=3236.21 KPa

We know that modulus of elasticity

[tex]E=\dfrac{dP}{-\dfrac{dV}{V}}[/tex]

[tex]E=\dfrac{3236.21-340}{-\dfrac{0.2-1}{1}}[/tex]

E=3620.26 KPa

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