Write the first law carefully with sign convention

The first law of thermodynamics is based on conservation of energy. Its form depends on the sign convention used.

• If $dW$ = work done by the system, then $dQ = dU + dW$
• If $dW$ = work done on the system, then work done by the system is $-dW$, so $dQ = dU - dW$

Check Assertion A

Assertion says:

If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively, then according to the first law, $dQ = dU - dW$

This is correct, because with $dW$ defined as work done on the system, $dU = dQ + dW$ which can be rearranged as $dQ = dU - dW$

So, Assertion A is true.

Check Reason R

Reason says:

First law of thermodynamics is based on law of conservation of energy.

This is true.

Does R explain A?

Yes. The equation in Assertion A is a mathematical statement of the first law, and the first law itself follows from conservation of energy. The exact sign depends on the work convention, but the underlying reason is indeed conservation of energy.

So, R is the correct explanation of A.

Final option

Therefore, the correct choice is: $\boxed{\text{B}}$

Both A and R are correct and R is the correct explanation of A.