Initial volume of 1 mole of a monoatomic gas is 2 litres. It is expanded isothermally to a volume of 6 litres. Change in internal energy is xR. Find x.
Correct Answer: 0
Solution and Explanation
Change in Internal Energy (\(\Delta U\)):
The change in internal energy for a thermodynamic process is given by:
\[ \Delta U = nC_V\Delta T \]
For an isothermal process, the temperature remains constant:
\[ \Delta T = 0 \]
Substituting \(\Delta T = 0\) into the equation:
\[ \Delta U = nC_V(0) \]
\[ \Delta U = 0 \]
Conclusion:
Since the process is isothermal, there is no change in the internal energy of the system.
Final Answer:
\(\Delta U = 0\)
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