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C_v for helium gas (He) is (in J mol^{-1} K^{-1})

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$C_{v}$ for helium gas $(He)$ is $(in J m o l^{- 1} K^{- 1})$

2.5

10.5

1.5

12.5

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C_{v}

for helium gas

(He)

(in J m o l^{- 1} K^{- 1})

9 mins ago

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Text solutionVerified

The internal energy of 1 mole of a gas at temperature

T

, having

f

degrees of freedom is given by ,

U = N_{A} \times (1/2) f k_{B} T = (1/2) f RT

......................eq1

where

N_{A} =

Avogadro's number

k_{B} =

Boltzmann's constant

from first law of thermodynamics ,

d U = d Q - d W

............eq2

At constant volume ,

d V = 0

hence

d W = P d V = 0

eq2 becomes ,

d U = d Q

but

d Q = C_{V} d T

(for 1 mole of gas)

therefore

d U = C_{V} d T

C_{V} = d U / d T

putting the value of

U

in this equation, we get

C_{V} = \frac{d ( 1/2 ) f RT}{d T} = \frac{f}{2} R

for Helium ,

f = 3

as it is a monatomic gas ,

hence

C_{V} = 3 R /2

we have

R = 8.31 J m o l^{- 1} K^{- 1}

Therefore

C_{V} = \frac{3 \times 8.31}{2} = 12.5 J m o l^{- 1} K^{- 1}

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Question Text	$C_{v}$ for helium gas $(He)$ is $(in J m o l^{- 1} K^{- 1})$
Answer Type	Text solution:1
Upvotes	150

Cv​ for helium gas (He) is (inJ mol−1 K−1)

Text solutionVerified

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