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  •  2 moles of an ideal gas <img alt="\left ( C_{v,m}=15\:JK^{-1}mol^{-1} \right )" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%20%28%20C_%7Bv%2Cm%7D%3D15%5C%3AJK%5E%7B-1%7Dmol%5E

 2 moles of an ideal gas \left ( C_{v,m}=15\:JK^{-1}mol^{-1} \right )  are at 300\: K and 5 \:L. If the gas is heated to 350 \:K and the volume changed to 15 \:L, Calculate the entropy (in J/K) change.

Option: 1

26.76


Option: 2

4.62


Option: 3

22.88


Option: 4

22.14


Answers (1)

best_answer

We have given,

Initial volume, V_1=5\:L

Final volume, V_2=15\:L

Initial Temperature, T_1 = 300\: K

Final Temperature, T_2 = 350 \:K

Number of moles, n = 2

Change in entropy as a function of T and V is given as,

\mathrm{\Delta S=nC_{v,m}\:In\frac{T_{2}}{T_{1}}+nR\:In\frac{V_{2}}{V_{1}}}

\mathrm{\Delta S=2\times15\times\:In\frac{350}{300}+2\times8.314\times\:In\frac{15}{5}}

\\\Delta S=4.62+18.26\\\\\Delta S=22.88\:J/K
 

Hence, option number (3) is correct

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mansi

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