SATHEE: Thermodynamics Question 262

Thermodynamics Question 262

Question: A mass of diatomic gas $(γ = 1.4)$ at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from $27^{\circ} C$ to $927^{\circ} C$ . The pressure of the gas in final state is

Options:

A) 28 atm

B) 68.7 atm

C) 256 atm

D) 8 atm

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $T_{1} = 273 + 27 = 300 K$

$T_{2} = 273 + 927 = 1200 K$

For adiabatic process, $P^{1 - γ} T^{γ} = constant \Rightarrow P_{1}^{1 - γ} T_{1}^{γ} = P_{2}^{1 - γ} T_{2}^{γ}$

$\Rightarrow {(\frac{P_{2}}{P_{1}})}^{1 - γ} = {(\frac{T_{1}}{T_{2}})}^{γ} \Rightarrow {(\frac{P_{1}}{T_{2}})}^{1 - γ} = {(\frac{T_{2}}{T_{1}})}^{γ}$

${(\frac{P_{2}}{P_{1}})}^{1 - 1.4} = {(\frac{1200}{300})}^{1.4} \Rightarrow {(\frac{P_{1}}{T_{2}})}^{- 0.4} = {(4)}^{1.4}$

${(\frac{P_{2}}{P_{1}})}^{0.4} = 4^{1.4} or, P_{2} = P_{1} 4^{(\frac{1.4}{0.4})} = P_{1} 4^{(\frac{7}{2})}$

$= P_{1} (2^{7}) = 2 \times 128 = 256 a t m$

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Thermodynamics Question 262

Question: A mass of diatomic gas (γ=1.4) at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from 27∘C to 927∘C . The pressure of the gas in final state is

Options:

Answer:

Solution:

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Question: A mass of diatomic gas $(γ = 1.4)$ at a pressure of 2 atmospheres is compressed adiabatically so that its temperature rises from $27^{\circ} C$ to $927^{\circ} C$ . The pressure of the gas in final state is