A system of ideal gas undergoes a thermodynamic process in which the initial pressure and volume are equal to the final pressure and volume. Let △Q is the heat supplied to the system,△W is the work done by the system and △U is the change in internal energy. The correct option is:
△Q=△W
△U>0
△U\(\neq\)0
△U+△Q+△W=0
△Q+△W=0
The Correct Option is A
Approach Solution - 1
Given conditions: \[ P_i = P_f \] \[ V_i = V_f \]
First Law of Thermodynamics: \[ \Delta U = \Delta Q - \Delta W \]
For ideal gas: \[ U = U(T) \text{ (depends only on temperature)} \]
From ideal gas equation: \[ PV = nRT \] \[ \text{Since } P_iV_i = P_fV_f \Rightarrow T_i = T_f \]
Internal energy change: \[ \Delta U = 0 \text{ (since temperature is constant)} \]
First Law becomes: \[ 0 = \Delta Q - \Delta W \] \[ \Delta Q = \Delta W \]
Approach Solution -2
1. Understand the thermodynamic process:
The problem states that the initial and final pressures and volumes are equal. This means the system undergoes a cyclic process, returning to its initial state.
2. Apply the first law of thermodynamics:
The first law of thermodynamics states:
\[\Delta U = \Delta Q - \Delta W\]
where:
- ΔU is the change in internal energy
- ΔQ is the heat supplied to the system
- ΔW is the work done by the system
3. Consider the cyclic process:
For a cyclic process, the system returns to its initial state, meaning the change in internal energy is zero:
\[\Delta U = 0\]
4. Analyze the options:
- (A) ΔQ = ΔW: Since ΔU = 0, the first law becomes \(0 = \Delta Q - \Delta W\), so ΔQ = ΔW. This is CORRECT.
- (B) ΔU > 0: ΔU = 0 for a cyclic process. This is INCORRECT.
- (C) ΔU ≠ 0: ΔU = 0 for a cyclic process. This is INCORRECT.
- (D) ΔU + ΔQ + ΔW = 0: Since ΔU = 0 and ΔQ = ΔW, this would imply 2ΔQ = 0, which is only true if no heat is exchanged. This can only occur if no work is also done. This is INCORRECT.
- (E) ΔQ + ΔW = 0: Since ΔQ = ΔW, this would imply 2ΔQ=0, which, as stated above can only occur if no heat and work are done, so this is INCORRECT
Final Answer: The correct option is \(\boxed{A}\)
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Concepts Used:
Laws of Thermodynamics
Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.
The First Law of Thermodynamics:
The first law of thermodynamics, also known as the Law of Conservation of Energy, states that energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another.
The Second Law of Thermodynamics:
The second law of thermodynamics says that the entropy of any isolated system always increases. Isolated systems spontaneously evolve towards thermal equilibrium—the state of maximum entropy of the system. More simply put: the entropy of the universe (the ultimate isolated system) only increases and never decreases.
The Third Law of Thermodynamics:
The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero. The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has. Specifically, the entropy of a pure crystalline substance (perfect order) at absolute zero temperature is zero