During a reversible isothermal compression, $0.5 \mathrm{~mol}$ of an ideal gas at $400 \mathrm{~K}$ is compressed from a pressure of $2 \mathrm{~atm}$ to $10 \mathrm{~atm}$ . What is the change in internal energy ( $\Delta U$ ) for the gas?
(Given: $\mathrm{R} = 8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ , $\log 5 = 0.699$ )

Question

During a reversible isothermal compression,

0.5 \mathrm{~mol}

of an ideal gas at

400 \mathrm{~K}

is compressed from a pressure of

2 \mathrm{~atm}

to

10 \mathrm{~atm}

. What is the change in internal energy (

\Delta U

) for the gas?
(Given:

\mathrm{R} = 8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}

,

\log 5 = 0.699

)

Quantrex Academy · Accepted Answer

Correct answer: C. 0 ~J

For an ideal gas, the internal energy depends only on its temperature.

In an isothermal process, the temperature of the system remains constant, which means

\Delta T = 0

.

The change in internal energy is given by the relation

\Delta U = n C_v \Delta T

.

Since

\Delta T = 0

, it follows that

\Delta U = 0 \mathrm{~J}

.

Answer:

0 \mathrm{~J}

During a reversible isothermal compression, 0.5 ~mol of an ideal...

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