Assertion : First law of thermodynamics does not forbid flow of heat from lower temperature to higher temperature.
Reason : Heat supplied to a system always equal to the increase in its internal energy.

Options

A. Both assertion and reason are true and reason is the correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assetion
C. Assertion is true but reason is false
D. Both assertion and reason are false.

Explanation

To solve the question, we will analyze the assertion and the reason provided, and determine their validity based on the principles of thermodynamics.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the first law of thermodynamics does not forbid the flow of heat from a lower temperature to a higher temperature.
- The first law of thermodynamics is expressed as:
\[ \Delta Q = \Delta U + W \]
- Here, \(\Delta Q\) is the heat added to the system, \(\Delta U\) is the change in internal energy, and \(W\) is the work done by the system.
- This law indicates the conservation of energy and does not impose restrictions on the direction of heat flow.

2. **Evaluating the Assertion**:
- According to the first law, heat can flow from a colder body to a hotter body if work is done on the system (for example, in refrigeration cycles).
- Therefore, the assertion is **true**.

3. **Understanding the Reason**:
- The reason states that the heat supplied to a system is always equal to the increase in its internal energy.
- This statement is not universally true. The relationship holds true only under specific conditions (e.g., when no work is done, i.e., \(dV = 0\)).
- In general, when work is done by or on the system, the heat supplied does not equal the change in internal energy.

4. **Evaluating the Reason**:
- Since the reason does not hold true in all situations (it requires specific conditions), the reason is **false**.

5. **Conclusion**:
- The assertion is true, while the reason is false.
- Therefore, the correct answer is that the assertion is true, but the reason is false.

### Final Answer:
- Assertion: True
- Reason: False