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An ideal gas undergoes isothermal and reversible expansion from its initial volume to some final volume at 300 K drawing in 90 kJ of heat. What is the change in gibbs free energy? a) 300 J b) 150 J c) 0 J d) -300 J?
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An ideal gas undergoes isothermal and reversible expansion from its in...
Answer:

Given:
- Isothermal and reversible expansion of an ideal gas
- Initial temperature (T) = 300 K
- Heat absorbed (q) = 90 kJ

To find:
- Change in Gibbs free energy (ΔG)

Solution:

We know that for isothermal and reversible processes,

ΔG = -TΔS + ΔH

Where,
- T is the temperature in Kelvin
- ΔS is the change in entropy
- ΔH is the change in enthalpy

Since the process is isothermal, the temperature (T) is constant. Therefore, ΔS = q/T, where q is the heat absorbed.

ΔS = q/T = 90 kJ / 300 K = 0.3 kJ/K

As the process is reversible, the change in enthalpy (ΔH) is equal to the heat absorbed (q).

ΔH = q = 90 kJ

Substituting these values in the equation for ΔG, we get:

ΔG = -TΔS + ΔH
ΔG = -(300 K)(0.3 kJ/K) + (90 kJ)
ΔG = -90 J + 90 kJ
ΔG = 89.91 kJ

Therefore, the change in Gibbs free energy is 89.91 kJ, which is equivalent to -300 J. Hence, the answer is option (d) -300 J.
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An ideal gas undergoes isothermal and reversible expansion from its initial volume to some final volume at 300 K drawing in 90 kJ of heat. What is the change in gibbs free energy? a) 300 J b) 150 J c) 0 J d) -300 J?
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