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Question Number 50275 by Tawa1 last updated on 15/Dec/18

	Answered by tanmay.chaudhury50@gmail.com last updated on 15/Dec/18

	$△ S = \int_{T_{1}}^{T_{2}} C_{v} \frac{d T}{T} - R \int_{V_{1}}^{V_{2}} \frac{d V}{V}$ $V_{1} = 1 \times 10^{- 3} m^{3} V_{2} = 3 \times 10^{- 3} m^{3}$ $R = 8.314$ $T_{1} = 100 K T_{2} = 400 K$ $C_{v} = 45 + 6 \times 10^{- 3} T + 8 \times 10^{- 6} T^{2}$ $△ S = \int_{T_{1}}^{T_{2}} (a + b T + {c T}^{2}) \frac{d T}{T} - R \int_{V_{1}}^{V_{2}} \frac{d V}{V}$ $=∣ a l n T + b T + c \times \frac{T^{2}}{2} ∣_{T_{1}}^{T_{2}} - R ∣ l n V ∣_{V_{1}}^{V_{2}}$ $= a l n (\frac{T_{2}}{T_{1}}) + b (T_{2} - T_{1}) + \frac{c}{2} (T_{2}^{2} - T_{1}^{2}) - R l n (\frac{V_{2}}{V_{1}})$ $= 45 l n (4) + 6 \times 10^{- 3} \times 300 + 4 \times 10^{- 6} \times 15 \times 10^{4} - 8.314 l n 3$ $= 45 l n 4 + 1.8 + 0.6 - 8.324 l n 3$ $= 2.4 + 45 l n 4 - 8.324 l n 3$ $\approx 55.64$
	Commented by Tawa1 last updated on 15/Dec/18

	$God bless you sir$
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