SATHEE: Thermodynamics - Result Question 23

Thermodynamics - Result Question 23

24. 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

(a) $28 a t m$

(b) $68.7 a t m$

(d) $8 a t m$

[2011M]

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Answer:

Correct Answer: 24. (c)

Solution:

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

For adiabatic process,

$P^{1 - γ} T^{γ} =$ constant

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

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

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

$\begin{aligned} \Rightarrow (\frac{P_{2}}{P_{1}})^{0.4} = 4^{1.4} \\ \Rightarrow P_{2} = P_{1} 4^{(\frac{1.4}{0.4})} = P_{1} 4^{(\frac{7}{2})} \\ \Rightarrow P_{1} (2^{7}) = 2 \times 128 = 256 a t m \end{aligned}$

Thermodynamics - Result Question 23

24. 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

Answer:

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Thermodynamics - Result Question 23

24. 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

Answer:

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24. 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