Question

Two moles of an ideal monoatomic gas occupies a volume V at ${27}^o$C. The gas expands adiabatically to a volume $2$V. Calculate (a) the final temperature of the gas and (b) change on its internal energy.

• A. (a) $189$K (b) $-2.7$ kJ
• B. (a) $195$K (b) $2.7$ kJ
• C. (a) $189$K (b) $2.7$kJ
• D. (a) $195$k (b) $-2.7$kJ

Answer 1

The correct option is A (a) $189$K (b) $-2.7$ kJ

In an adiabatic process, $P{V}^{\gamma }=constant$

or $T{V}^{\gamma -1}=constant$

$\frac{T_2}{T_1}=(\frac{V_1}{V_2}{)}^{\gamma -1}$

For monoatomic gas

$\gamma =\frac{5}{3}$

$T_2=\left(300K\right)(\frac{V}{2V}{)}^{\frac{5}{3}-1}$

$=189K$

Change in internal energy

$\Delta U=n{C}_v\Delta T$

$=2\left(\frac{3}{2}\right)\left(\frac{25}{3}\right)(-111)$

$=-2.7kJ$