Question

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

Answer 1

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Answer 2

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 $\frac{3W}{2}$ .

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