A gas at 17° has the ratio of its initial to final volume as 25 with initial pressure of 2×10^5 Nm^(−2) .Calculate the final pressure and temperature after compression.(γ=1.5)


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Question Number 40498 by Necxx last updated on 23/Jul/18

$A g a s a t 17 ° h a s t h e r a t i o o f i t s i n i t i a l$ $t o f i n a l v o l u m e a s 25 w i t h i n i t i a l$ $p r e s s u r e o f 2 \times 10^{5} {N m}^{- 2} . C a l c u l a t e$ $t h e f i n a l p r e s s u r e a n d t e m p e r a t u r e$ $a f t e r c o m p r e s s i o n . (γ = 1.5)$
	Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jul/18

	${p v}^{γ} = c o n s t a n t$ $p_{1} v_{1}^{γ} = p_{2} v_{2}^{γ} p_{2} = p_{1} {(\frac{v_{1}}{v_{2}})}^{γ}$ $p_{2} = 2 \times 10^{5} . {(25)}^{1.5}$ $p_{1} v_{1} v_{1}^{γ - 1} = p_{2} v_{2} v_{2}^{γ - 1}$ ${R T}_{1} v_{1}^{γ - 1} = {R T}_{2} v_{2}^{γ - 1}$ $T_{2} = T_{1} {(\frac{v_{1}}{v_{2}})}^{γ - 1}$ $T_{2} = (273 + 17) . {(25)}^{0.5}$
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