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Thermodynamics question

2019 · 8 Apr · Shift 2 · Q8
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Thermodynamics question

2019 · 8 Apr · Shift 2 · Q8

JEE MainChemistryThermodynamicsMCQ+4 / −1
5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If CV = 28 JK–1mol–1, calculate Δ\DeltaΔ U and Δ\DeltaΔ pV for this process. (R = 8.0 JK–1 mol–1]
  1. A
    Δ\DeltaΔ U = 14 kJ; Δ\DeltaΔ(pV) = 4 kJ
  2. B
    Δ\DeltaΔ U = 2.8 kJ; Δ\DeltaΔ(pV) = 0.8 kJ
  3. C
    Δ\DeltaΔ U = 14 kJ; Δ\DeltaΔ(pV) = 18 kJ
  4. D
    Δ\DeltaΔ U = 14 kJ; Δ\DeltaΔ(pV) = 0.8 kJ
View written solutionFree

Correct answer: A

  1. Given data
  • Number of moles: n=5n = 5n=5
  • Initial temperature: T1=100 KT_1 = 100\,\text{K}T1​=100K
  • Final temperature: T2=200 KT_2 = 200\,\text{K}T2​=200K
  • Molar heat capacity at constant volume: CV=28 J K−1mol−1C_V = 28\,\text{J K}^{-1}\text{mol}^{-1}CV​=28J K−1mol−1
  • Gas constant: R=8 J K−1mol−1R = 8\,\text{J K}^{-1}\text{mol}^{-1}R=8J K−1mol−1

So,

ΔT=T2−T1=200−100=100 K\Delta T = T_2 - T_1 = 200 - 100 = 100\,\text{K}ΔT=T2​−T1​=200−100=100K
  1. Calculate change in internal energy, ΔU\Delta UΔU

For an ideal gas,

ΔU=nCVΔT\Delta U = n C_V \Delta TΔU=nCV​ΔT

Substituting values,

ΔU=5×28×100\Delta U = 5 \times 28 \times 100ΔU=5×28×100 ΔU=14000 J=14 kJ\Delta U = 14000\,\text{J} = 14\,\text{kJ}ΔU=14000J=14kJ

Thus,

ΔU=14 kJ\boxed{\Delta U = 14\,\text{kJ}}ΔU=14kJ​
  1. Calculate change in pVpVpV

For an ideal gas,

pV=nRTpV = nRTpV=nRT

Hence change in pVpVpV is,

Δ(pV)=nRΔT\Delta(pV) = nR\Delta TΔ(pV)=nRΔT

Substituting values,

Δ(pV)=5×8×100\Delta(pV) = 5 \times 8 \times 100Δ(pV)=5×8×100 Δ(pV)=4000 J=4 kJ\Delta(pV) = 4000\,\text{J} = 4\,\text{kJ}Δ(pV)=4000J=4kJ

Thus,

Δ(pV)=4 kJ\boxed{\Delta(pV) = 4\,\text{kJ}}Δ(pV)=4kJ​
  1. Match with options

The values obtained are:

  • ΔU=14 kJ\Delta U = 14\,\text{kJ}ΔU=14kJ
  • Δ(pV)=4 kJ\Delta(pV) = 4\,\text{kJ}Δ(pV)=4kJ

This matches:

Option A\boxed{\text{Option A}}Option A​
  1. Comparison with stored correct answer

Stored correct answer: A

Our derived answer: A

So they agree.

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