MHT CET · Chemistry · Thermodynamics (C)
An ideal gas expands against constant external pressure of 2 bar from 5 lit to 8 lit and absorbs 10 kJ of heat. What is \(\Delta \mathrm{U}\) of the system?
- A 10600 J
- B 9400 J
- C -10600 J
- D -9400 J
Answer & Solution
Correct Answer
(B) 9400 J
Step-by-step Solution
Detailed explanation
\(W=-P_{\text {ext }} \times \Delta V=-2 \times(8-5)=-6 \mathrm{~L} \text { bar } \)
\( 1 \mathrm{~L} \mathrm{bar}=100 \mathrm{~J} \)
\( \therefore W=-600 \mathrm{~J}=-0.6 \mathrm{~kJ} \quad(\because 1 \mathrm{~kJ}=1000 \mathrm{~J}) \)
\( Q=+10 \mathrm{~kJ}\)
According to the first law of thermodynamics,
\(\begin{aligned}
& \Delta \mathrm{U}=\mathrm{Q}+\mathrm{W} \\
& \therefore \Delta \mathrm{U}=+10 \mathrm{~kJ}+(-0.6 \mathrm{~kJ})=9.4 \mathrm{~kJ}=9400 \mathrm{~J}
\end{aligned}\)
\( 1 \mathrm{~L} \mathrm{bar}=100 \mathrm{~J} \)
\( \therefore W=-600 \mathrm{~J}=-0.6 \mathrm{~kJ} \quad(\because 1 \mathrm{~kJ}=1000 \mathrm{~J}) \)
\( Q=+10 \mathrm{~kJ}\)
According to the first law of thermodynamics,
\(\begin{aligned}
& \Delta \mathrm{U}=\mathrm{Q}+\mathrm{W} \\
& \therefore \Delta \mathrm{U}=+10 \mathrm{~kJ}+(-0.6 \mathrm{~kJ})=9.4 \mathrm{~kJ}=9400 \mathrm{~J}
\end{aligned}\)
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