Science, asked by panjwani4680, 1 year ago

For a monatomic gas work done at constant pressure is w. the heat supplied at constant volume for the same

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Answered by Anonymous
4
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Answered by gayatrikumari99sl
1

Answer:

The heat supplied at constant volume for the same rise in temperature of the gas is \frac{3W}{2} .

Explanation:

Given , a monatomic gas work done at constant pressure w .

And the heat supplied at constant volume .

Step 1:

For constant pressure  ,

Q = C_{p}ΔT +W

(where Cp is heat capacity and ΔT is change in temperature )

⇒ ΔT = \frac{(Q-W)}{C_{p}}

Now ,  at constant volume ;

Q = C_{v}ΔT                   (work done is zero )

⇒Q = C_{v}[\frac{(Q-W)}{C_{p}}]

\frac{C_{p} }{C_v}  Q = Q- W

But we know  \frac{C_{p} }{C_v} is equal to γ

Therefore ,

γQ = Q- W

⇒Q (γ - 1) = -W

⇒Q (\frac{5}{3} - 1 ) = -W                        (Where γ = \frac{5}{3} for monatomic gas )

\frac{2}{3} Q = -W

⇒Q = \frac{-3W}{2}

⇒|Q| = \frac{3W}{2}

Hence , the heat supplied at constant volume for the same rise in temperature of the gas is \frac{3W}{2} .

#SPJ2

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