Internal Energy

Step 1: Understanding the relationship between energy and ideal gas expansion.
For an ideal gas undergoing an expansion at constant temperature and pressure, the internal energy remains unchanged because the temperature does not change. The internal energy of an ideal gas is only a function of temperature.

Step 2: Explanation of the options.
- (1) Internal energy remains same: This is correct because for an ideal gas, internal energy depends only on temperature, which remains constant in this process.
- (2) Internal energy decreases: Incorrect. The internal energy does not change in an isothermal process.
- (3) Internal energy increases: Incorrect. Again, internal energy does not change at constant temperature.
- (4) Entropy first increases and then decreases: This is incorrect. Entropy increases during expansion, but it doesn't decrease.

Step 3: Conclusion.
The correct answer is (1) Internal energy remains same.

Step 1: Understanding the relationship between and .
The relationship between enthalpy ( ) and internal energy ( ) is given by: where is the change in the number of moles of gas.

Step 2: Calculating .
For the formation of CO from its elements at 298 K, (since one mole of CO gas is formed). Using the ideal gas constant : Thus, the correct answer is .

Step 3: Conclusion.
The correct answer is (1) .

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}




Step 3: Final Answer

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}
Cetyl trimethyl ammonium bromide ( ) has head group (cationic).
Sodium dodecyl sulphate is anionic. Sodium acetate and urea do not form micelles.
Step 3: Final Answer

Concept: In a cyclic process, the system returns to its initial state.

Step 1: Internal energy.
Since internal energy is a state function:

Step 2: First law.
This is always valid, but not specific to cyclic process.

Step 3: Conclusion.
Only the defining property of a cyclic process is:

Concept:

Step 1: Condition.
when

Step 2: Check reactions.
(A) change in moles
(B)
(C) \checkmark
(D) gas to liquid

Step 3: Conclusion.
Correct option is (C)

Concept:

Step 1: Convert units to Joules.

Step 2: Substitute into formula.

Step 3: Solve for .

Concept: First law of thermodynamics:

Step 1: Convert volume.


Step 2: Work done.


Step 3: Apply formula.

Concept:
•Helmholtz free energy ( ) is used for processes at constant temperature and volume.
•The decrease in Helmholtz free energy gives the maximum work obtainable.

Step 1: Condition For a reversible process at constant temperature and volume:

Step 2: Conclusion