A) +2.8 J/K
B) -22.1 J/K
C) +24.9 J/K
D) None of the above
Correct Answer: A
Solution :
Let the final temperature of the system be \[{{t}^{o}}C\] Heat lost = Heat gain \[\therefore \] \[0.05\times 180+4.18\times {{10}^{3}}\times 0.05(t-20)\] \[=0.2\times 900\,(100-t)\] \[209+180t=1800+4180-9\] 389 t =22171 \[t={{56.99}^{o}}C\] \[t={{57}^{o}}C\] \[{{S}_{1}}=\frac{mQ}{T}+mc\log \left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)\] \[=\frac{0.05\times 180}{273}+0.05\times 4.18\times {{10}^{3}}\log \left( \frac{57+273}{20+273} \right)\] \[=\frac{9}{273}+209\log \frac{330}{293}\] \[=0.032+209\times 0.0596\] \[=0.032+12.4564\] = 12.4884 \[{{S}_{2}}=mc\log \left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)\] \[=0.20\times 900\log \left( \frac{57+273}{100+273} \right)\] \[=180\log \frac{330}{373}\] \[=-180\times (0.0532)\] = - 9.576 So, change entropy \[={{S}_{1}}+{{S}_{2}}\] = 12.4884 - 9.576 = 2.91 J/K \[\cong \] + 2.8 J/K
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