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170 kJ of heat is supplied to a system at constant volume. Then the system rejects 180 kJ of heat at constant pressure and 40 kJ of work is done on it. The system is finally brought to its original state by adiabatic process. If the initial value of internal energy is 100 kJ, then which one of the following statements is correct?
  • a)
    The highest value of internal energy occurs at the end of the constant volu me process
  • b)
    The highest value of internal energy occurs at the end of constant pressure process.
  • c)
    The highest value of internal energy occurs after adiabatic expansion
  • d)
    Internal energy is equal at all points
Correct answer is option 'A'. Can you explain this answer?
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Given information:
- Heat supplied at constant volume = 170 kJ
- Heat rejected at constant pressure = 180 kJ
- Work done on the system = 40 kJ
- Initial internal energy = 100 kJ

To determine:
At which point does the system have the highest value of internal energy?

Solution:
Firstly, let's analyze the given information and determine the changes in internal energy at each point.

1. Constant volume process:
- Heat supplied at constant volume = Increase in internal energy
- ΔU = 170 kJ

2. Constant pressure process:
- Heat rejected at constant pressure = Decrease in internal energy
- ΔU = -180 kJ

3. Work done on the system:
- Work done on the system = Decrease in internal energy
- ΔU = -40 kJ

4. Adiabatic process:
- Adiabatic process means no heat transfer occurs, hence no change in internal energy.
- ΔU = 0

Now, let's add up the changes in internal energy at each point to determine the final value of internal energy.

ΔU_total = ΔU1 + ΔU2 + ΔU3 + ΔU4

ΔU_total = 170 - 180 - 40 + 0

ΔU_total = -50 kJ

As the total change in internal energy is negative, this means that the final internal energy is less than the initial internal energy. Therefore, options C and D can be eliminated.

Now, we need to determine whether the highest value of internal energy occurs at the end of the constant volume process or the end of the constant pressure process.

- Option A: The highest value of internal energy occurs at the end of the constant volume process. This option is correct because the system gains internal energy during the constant volume process and there is no other process that can compensate for this gain in internal energy.

- Option B: The highest value of internal energy occurs at the end of the constant pressure process. This option is incorrect because the system loses internal energy during the constant pressure process and there is no other process that can compensate for this loss in internal energy.

Therefore, the correct answer is option A.

Summary:
- The highest value of internal energy occurs at the end of the constant volume process.
- The total change in internal energy is negative, hence the final internal energy is less than the initial internal energy.
- Adiabatic process means no change in internal energy.
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170 kJ of heat is supplied to a system at constant volume. Then the system rejects 180 kJ of heat at constant pressure and 40 kJ of work is done on it. The system is finally brought to its original state by adiabatic process. If the initial value of internal energy is 100 kJ, then which one of the following statements is correct?a)The highest value of internal energy occurs at the end of the constant volu me processb)The highest value of internal energy occurs at the end of constant pressure process.c)The highest value of internal energy occurs after adiabatic expansiond)Internal energy is equal at all pointsCorrect answer is option 'A'. Can you explain this answer?
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