SATHEE: Thermodynamics Question 268

Thermodynamics Question 268

Question: Calculate the work done when 1 mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are $10^{5} N / m^{2}$ and 6 liter respectively. The final volume of the gas is 2 liters. Molar specific heat of the gas at constant volume is 3R/2.

[Given ${(3)}^{5 / 3} = 6.19$ ]

Options:

A) -957 J

B) +957 J

C) -805 J

D) + 805 J.

Show Answer

Answer:

Correct Answer: A

Solution:

[a] For an adiabatic change $P V^{γ} = c o n s t a n t$

$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

As molar specific heat of gas at constant volume $C_{v} = \frac{3}{2} R$

$C_{p} = C_{V} + R = \frac{3}{2} R + R = \frac{5}{2} R;$

$γ = \frac{C_{p}}{C_{V}} = \frac{(5 / 2) R}{(3 / 2) R} = \frac{5}{3}$

$∴$

From $e q^{n} . (1)$

$P_{2} = {(\frac{V_{1}}{V_{2}})}^{γ} P_{1} = {(\frac{6}{2})}^{5 / 3} \times 10^{5} N / m^{2}$

$= {(3)}^{5 / .3} \times 10^{5} = 6.19 \times 10^{5} N / m^{2}$ Work done $= \frac{1}{1 - (5 / 3)}$

$[6.19 \times 10^{5} \times 2 \times 10^{- 3} - 10^{- 5} 6 \times 10^{- 3}]$

$= - 3 \times 10^{2} \times 3.19 = - 957 joules$ [-ve sign shows external work done on the gas]

Thermodynamics Question 268

Question: Calculate the work done when 1 mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are $10^{5} N / m^{2}$ and 6 liter respectively. The final volume of the gas is 2 liters. Molar specific heat of the gas at constant volume is 3R/2.

Options:

Answer:

Solution:

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Thermodynamics Question 268

Question: Calculate the work done when 1 mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are 105N/m2 and 6 liter respectively. The final volume of the gas is 2 liters. Molar specific heat of the gas at constant volume is 3R/2.

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: Calculate the work done when 1 mole of a perfect gas is compressed adiabatically. The initial pressure and volume of the gas are $10^{5} N / m^{2}$ and 6 liter respectively. The final volume of the gas is 2 liters. Molar specific heat of the gas at constant volume is 3R/2.