Question

A system has internal energy equal to \[{{E}_{1}}\], 450 J of heat is taken out from it and 500 J of work done on it. The final energy of the system will be
(A) (\[{{E}_{1}}\]+150)
(B) (\[{{E}_{1}}\]+1050)
(C) (\[{{E}_{1}}\]-150)
(D) None of the above

Answer 1

Hint: Internal energy is one of the thermodynamics properties of a system. In this, the system refers to the part of the universe which is under study. Surrounding is the rest of the system.
Universe=system+surrounding.

Complete step by step solution:
-There are 3 types of system. Systems which can exchange both energy and matter are called open systems. All living systems are open systems. Systems which can exchange energy and not matter are called closed systems. Eg, heating of water in a closed container. Systems which cannot exchange either energy or matter are called isolated systems. Eg, water in a thermos.
-State functions are the property of a system. They depend only on the state of the system and not on the path adopted to achieve such a state. Temperature, pressure, volume, total internal energy, enthalpy, entropy, Gibbs free energy are state functions.
-System exchanges energy by 2 modes – heat and work. Both are forms of energy. When energy is transferred as a result of temperature difference, it is called heat. When energy is transferred not due to temperature differences, it is called work.
-Energy given to the system is considered positive. So heat given to the system is positive and heat taken out of the system is negative. Work done on the system is positive and work done by the system is negative.
$\Delta U=\Delta Q+\Delta W$
-In the above question, we can see that the internal energy is given as \[{{E}_{1}}\]. 500J of work is done on the system. So, it is a positive value.
$\Rightarrow \Delta W=+500J$
450J of heat is taken out of the system. So, it will be negative.
$\Delta Q=-450J$
-Initial energy was \[{{E}_{1}}\]. Now the total energy will be given as
U=\[{{E}_{1}}\]+$\Delta U$
$\Delta U=\Delta Q+\Delta W$
$= +500J – 450J$
$= +50J$
So, the total energy of the system will now become \[{{E}_{1}}\]+50J

Therefore the correct option is D. None of the above.

Note: Internal energy of the system depends on the actual state of the system. It doesn’t depend on how that state is achieved. Always keep in mind that work done on the system is positive and work done by the system is negative in chemistry.