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Thermodynamics question

2020 · 8 Jan · Shift 2 · Q8
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Thermodynamics question

2020 · 8 Jan · Shift 2 · Q8

JEE MainChemistryThermodynamicsNumerical+4 / −1
At constant volume, 4 mol of an ideal gas when heated from 300 K to 500K changes its internal energy by 5000 J. The molar heat capacity at constant volume is ‾\underline{\hspace{2cm}}​.
Numerical answer
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Correct answer: 6.25

  1. For an ideal gas, the change in internal energy at constant volume is

ΔU=nCV,mΔT\Delta U = n C_{V,m} \Delta TΔU=nCV,m​ΔT

where:

  • ΔU=5000 J\Delta U = 5000\,\text{J}ΔU=5000J
  • n=4 moln = 4\,\text{mol}n=4mol
  • ΔT=500−300=200 K\Delta T = 500 - 300 = 200\,\text{K}ΔT=500−300=200K
  • CV,mC_{V,m}CV,m​ = molar heat capacity at constant volume
  1. Substitute the values:

5000=4⋅CV,m⋅2005000 = 4 \cdot C_{V,m} \cdot 2005000=4⋅CV,m​⋅200

5000=800CV,m5000 = 800 C_{V,m}5000=800CV,m​

  1. Solve for CV,mC_{V,m}CV,m​:

CV,m=5000800=6.25 J mol−1K−1C_{V,m} = \frac{5000}{800} = 6.25\,\text{J mol}^{-1}\text{K}^{-1}CV,m​=8005000​=6.25J mol−1K−1

  1. Therefore, the molar heat capacity at constant volume is

6.25 J mol−1K−1\boxed{6.25\,\text{J mol}^{-1}\text{K}^{-1}}6.25J mol−1K−1​

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