Question

The internal energy of a gas is 20 J. It undergoes
a thermodynamic process such that 35 J of heat
is added to the system and it does 5 J of work on
atmosphere. The final value of the internal energy
of the gas is​

Answer 1

The final value of the internal energy of the gas is 50 J.​

Explanation:

1. From first law of thermodynamics equation

   $Q_{1-2}=U_{f}-U_{i}+W_{1-2}$     ...1)

  where

  $W_{1-2}$ = amount of work interaction = +5 J

  $Q_{1-2}$ = amount of heat interaction = +35 J

  $U_{f}$ = final internal energy of system =?

  $U_{i}$ = final internal energy of system =20 J

2. $W_{1-2}$ = amount of work interaction = +5 J

   Here positive sign is taken because work is done by system.

3. $Q_{1-2}$ = amount of heat interaction = +35 J

   Here positive sign is taken because heat is given to system.

4. Now from equation 1)

     $Q_{1-2}=U_{f}-U_{i}+W_{1-2}$

     $+35=U_{f}-20+5$

   On solving

     $U_{f}$ = 50 J = Final internal energy of system.