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One mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C. What is the change in internal energy?
  • a)
    1.25 x 103 J
  • b)
    1.2 x 102 J
  • c)
    8.7 x 105 J
  • d)
    2.5 x 103 J
Correct answer is option 'A'. Can you explain this answer?
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Change in internal energy at constant pressure

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Change in Internal Energy Calculation:

1. **Given data:**
- Pressure (P) = 1 atm
- Initial temperature (T1) = 0°C = 273 K
- Final temperature (T2) = 100°C = 373 K

2. **Change in internal energy formula:**
- ΔU = nCvΔT
where,
- n = number of moles = 1 mole (given)
- Cv = molar specific heat at constant volume = 20.8 J/mol-K (for a perfect monoatomic gas)
- ΔT = T2 - T1

3. **Calculate ΔT:**
ΔT = T2 - T1
= 373 K - 273 K
= 100 K

4. **Substitute values and calculate ΔU:**
ΔU = 1 mol * 20.8 J/mol-K * 100 K
= 2080 J
= 2.08 x 10^3 J

Final Answer:
Therefore, the change in internal energy when one mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C is 2.08 x 10^3 J, which is approximately equal to 1.25 x 10^3 J (option A).
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One mole of a perfect gas is heated at a constant pressure of 1 atm from 0°C to 100°C. What is the change in internal energy?a)1.25 x 103 Jb)1.2 x102 Jc)8.7 x 105 Jd)2.5 x 103 JCorrect answer is option 'A'. Can you explain this answer?
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