Question

$5$ moles of an ideal gas at $100\, K$ are allowed to undergo reversible compression till its temperature becomes $200\, K$. If $C_{V} =28 JK^{-1}mol^{-1} , caculate \Delta\, U$ and $\Delta \,pV $ for this process. ($R = 8.0 \, JK^{-1}mol^{-1}$]

• A. $ \Delta U = 14\, kJ: \Delta\left(pV\right) = 4\, kJ$
• B. $ \Delta U = 14\, kJ: \Delta\left(pV\right) = 18\, kJ$
• C. $ \Delta U = 2.8\, kJ: \Delta\left(pV\right) = 0.8\, kJ$
• D. $ \Delta U = 14\, kJ: \Delta\left(pV\right) = 0.8\, kJ$

Answer 1

Answer: (A)

$\Delta U=nC_{V}m\times\Delta T$
$= 5 \times 28 \times 100 = 14\, kJ$
$\Delta PV=nR\Delta T$
$=5\times 8\times 100=4\, kJ$