With what minimum pressure (in $kPa$ ), a given volume of an ideal gas $(C_{p . m} = \frac{7}{2} R)$ , originally at $400 K$ and $100 kPa$ pressure can compressed irreversibly adiabatically in order to raise its temperature to $600 K$ ?

362.5 pKa

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275 pKa

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437.5 pKa

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550 pKa

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Solution

The correct option is B $275 pKa$
Given
$C_{p . m} = \frac{7}{2} R$
$∴ C_{v, m} = \frac{5}{2} R$
For an adiabatic irreversible compression,
$Δ U = w n C_{v, m} (T_{2} - T_{1}) = P_{e x t} (V_{2} - V_{1}) Here P_{e x t} = P_{2} n C_{v, m} (T_{2} - T_{1}) = - P_{2} [\frac{n R T_{2}}{P_{2}} - \frac{n R T_{1}}{P_{1}}] \Rightarrow \frac{5}{2} R (T_{2} - T_{1}) = - P_{2} \times R [\frac{T_{2}}{P_{2}} - \frac{T_{1}}{P_{1}}] \Rightarrow P_{2} = 275 pKa$

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Similar questions

With what minimum pressure (in kPa), a given volume of an ideal gas $(C_{p, m} = \frac{7}{2} R),$ originally at 400 K and 100 kPa pressure can be compressed irreversibly and adiabatically in order to raise its temperature to 600 K:

N_{2}

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N_{2}

originally at 373 k and 0.1013 M pa pressure is adiabatically compressed due to which its temperature rises to

673 K (C v = \frac{5}{2} R)

Which of the following statement(s) is/are correct?

Q. An ideal gas at pressure 2.5 × 10⁵ Pa and temperature 300 K occupies 100 cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure (b) the final temperature and (c) the work done by the gas in the process. Take γ = 1.5

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An ideal gas at pressure $2.5 \times 10^{5}$ Pa and temperature 300 K occupies 100 cc. It is adiabatically compresses to half its original volume. Calculate

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(b) The final temperature and

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With what minimum pressure (in kPa), a given volume of an ideal gas (Cp.m=72R), originally at 400 K and 100 kPa pressure can compressed irreversibly adiabatically in order to raise its temperature to 600 K?

The correct option is B 275 pKaGiven Cp.m=72R ∴ Cv,m=52R For an adiabatic irreversible compression, ΔU=wnCv,m(T2−T1)=Pext(V2−V1)Here Pext=P2nCv,m(T2−T1)=−P2[nRT2P2−nRT1P1]⇒52R(T2−T1)=−P2×R[T2P2−T1P1]⇒P2=275 pKa

With what minimum pressure (in $kPa$ ), a given volume of an ideal gas $(C_{p . m} = \frac{7}{2} R)$ , originally at $400 K$ and $100 kPa$ pressure can compressed irreversibly adiabatically in order to raise its temperature to $600 K$ ?