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A heat engine absorbs heat q(1) from a s...

A heat engine absorbs heat `q_(1)` from a source at temperature `T_(1)` and heat `q_(2)` from a source at temperature `T_(2)`. Work done is found to be `J (q_(1) + q_(2))`. This is in accordance with

A

First law of thermodynamics

B

Second law of thermodynamics

C

Joules equivalent law

D

None of the above

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these logical steps: ### Step 1: Understand the Problem We have a heat engine that absorbs heat \( q_1 \) from a source at temperature \( T_1 \) and heat \( q_2 \) from another source at temperature \( T_2 \). The work done by the engine is given as \( J(q_1 + q_2) \). ### Step 2: Define Total Heat Absorbed Let’s define the total heat absorbed by the engine: \[ Q = q_1 + q_2 \] This represents the total heat absorbed from both sources. ### Step 3: Relate Work Done to Heat Absorbed According to the problem, the work done \( W \) is given by: \[ W = J(q_1 + q_2) = JQ \] This means that the work done by the heat engine is proportional to the total heat absorbed. ### Step 4: Recall Joule's Law Joule's law states that the work done by a heat engine is proportional to the heat absorbed. Mathematically, it can be expressed as: \[ Q = W/J \] From this, we can rearrange it to find: \[ W = JQ \] This is consistent with our earlier expression for work done. ### Step 5: Conclusion Since the relationship established is consistent with Joule's law, we conclude that the work done by the heat engine in absorbing heat \( q_1 \) and \( q_2 \) is in accordance with Joule's equivalent law. ### Final Answer Thus, the correct answer is that this is in accordance with **Joule's Law**. ---
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