Which of the following statements is true? | PGMN Solutions

Which of the following statements is true?
(ΔU = increase in internal energy, dW = work done by the system)
(A) In an adiabatic process, ΔU = dW
(B) In an adiabatic process, ΔU = –dW
(C) In an isothermal process, ΔU = –dW
(D) In an isothermal process, ΔU = dW
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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Thermodynamics
📌 Topic: First Law of Thermodynamics and Process-Based Energy Relations

🔹 Step 1: Understand the first law of thermodynamics
The first law states:
Change in internal energy = Heat supplied – Work done by the system
That is,
ΔU = Q – dW

🔹 Step 2: Analyze the adiabatic process
In an adiabatic process, there is no heat exchange with the surroundings.
So, Q = 0

Putting Q = 0 in the first law:
ΔU = –dW

This means, any work done by the gas (positive dW) results in a decrease in internal energy, and vice versa.

🔹 Step 3: Analyze the isothermal process
In an isothermal process, temperature remains constant, and for an ideal gas, internal energy depends only on temperature.
So, if temperature doesn’t change,
ΔU = 0

Putting ΔU = 0 in the first law:
0 = Q – dW → Q = dW

This means all heat supplied is used to do work, but internal energy doesn’t change.

🔹 Step 4: Evaluate the given options

(A) ΔU = dW → ❌ Incorrect for adiabatic

(B) ΔU = –dW → ✅ Correct for adiabatic

(C) ΔU = –dW → ❌ Incorrect for isothermal (ΔU = 0)

(D) ΔU = dW → ❌ Incorrect for isothermal (ΔU = 0)

✅ Final Answer: (B) In an adiabatic process, ΔU = –dW 🚀
🔥 Pro Tip:

For adiabatic: Heat Q = 0 → ΔU = –dW

For isothermal: ΔU = 0 → Heat supplied = Work done

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