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Heat, internal energy and work

5.6 litre of helium gas at STP is adiabatically compressed to

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Hard

Solving time: 5 mins

$5.6$ litre of helium gas at STP is adiabatically compressed to $0.7$ litre. Taking the initial temperature to be $T_{1}$ , the work done in the process is

\frac{9}{8} R T_{1}

\frac{3}{2} R T_{1}

\frac{15}{8} R T_{1}

\frac{9}{2} R T_{1}

Views: 5,488 students

Updated on: Feb 26, 2023

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Luna Discussed

5.6

litre of helium gas at STP is adiabatically compressed to

0.7

litre. Taking the initial temperature to be

T_{1}

, the work done in the process is

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Initially,

V_{1} = 5.6 l i t er

T_{1} = 273 K, P_{1} = 1 atm

γ = \frac{5}{3}

(For monatomic gas)
The number of moles of gas is

n = \frac{5.6 ℓ}{22.4 ℓ} = \frac{1}{4}

Finally (after adiabatic compression)

V_{2} = 0.7 l i t er

For adiabatic compression

T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}

∴ T_{2} = T_{1} (\frac{V _{1}}{V _{2}})^{y - 1} = T_{1} (\frac{5.6}{0.7})^{\frac{5}{3} - 1} = T_{1} (8)^{2/3} = 4 T_{1}

We know that work done in adiabatic process is

W = \frac{n R Δ T}{γ - 1} = \frac{9}{8} R T_{1}

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Question Text	$5.6$ litre of helium gas at STP is adiabatically compressed to $0.7$ litre. Taking the initial temperature to be $T_{1}$ , the work done in the process is
Updated On	Feb 26, 2023
Topic	Thermodynamics
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	756
Avg. Video Duration	11 min

$5.6$ litre of helium gas at STP is adiabatically compressed to $0.7$ litre. Taking the initial temperature to be $T_{1}$ , the work done in the process is

Text solutionVerified

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$5.6$ litre of helium gas at STP is adiabatically compressed to $0.7$ litre. Taking the initial temperature to be $T_{1}$ , the work done in the process is