Question

If W is work done by the system (-ve), the mathematical representation of the first law of thermodynamics is/are

• A. $\Delta U=\Delta q-W$
• B. $q=\Delta U-W$
• C. $dq+dW=0$
• D. $\Delta U=q+W$

Answer 1

Answer: (B), (D)

The correct options are
B $q=\Delta U-W$
D $\Delta U=q+W$

First law of thermodynamics states that energy is conserved. Direct consequence of this statement is U is state function. This implies between any two fixed state, there can be infinite process or path, but $\Delta U$ in all process will remain the same.(Property of a function of state).
Mathematical expression:
$\Delta U=q+w,$ i.e., the internal energy of system is equal to the sum of heat and work.