5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K.

If $C_V = 28\,\text{J K}^{-1}\text{mol}^{-1}$ and $R = 8.0\,\text{J K}^{-1}\text{mol}^{-1})$ , the values of $\Delta U$ and $\Delta(pV)$ for this process are:

Question

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K.

If $C_V = 28\,\text{J K}^{-1}\text{mol}^{-1}$ and $R = 8.0\,\text{J K}^{-1}\text{mol}^{-1})$ , the values of $\Delta U$ and $\Delta(pV)$ for this process are:

Paaras Thakur · Accepted Answer

U=14\,kJ;(pV)=4\,kJ. 🧠 U = nCv T and (pV) = nR T — two separate formulas For any ideal gas process: U uses Cv; (pV) = (nRT) = nR T. 🗺️ Calculation n = 5 mol, Cv = 28 J K-1mol-1, R = 8.0 J K-1mol-1, T = 200 - 100 = 100 K U = nC_v T = 5 28 100 = 14000{ J} = 14{ kJ} (pV) = nR T = 5 8.0 100 = 4000{ J} = 4{ kJ} Check: H = U + (pV) = 14 + 4 = 18 kJ ✓ ⚠️ Trap: Don't add (pV) to U when calculating (pV) itself. They are separate quantities; (pV) uses R, not Cp. {{Answer: (b)}}

Answer

U=14\,J;(pV)=0.8\,J

Answer

U=14\,kJ;(pV)=4\,kJ

Answer

U=14\,kJ;(pV)=18\,kJ

Answer

U=2.8\,kJ;(pV)=0.8\,kJ

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If…

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