Question

A gas is cooled and loses 50J of heat. The gas contracts as it cools and work done on the system equals 20J is exchanged with the surroundings and hence, $\Delta E$ is:
A. 70 J
B. -30 J
C. 30 J
D. -70 J

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 answer:
-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 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 20J of work is done on the system. So, it is a positive value.
$\Rightarrow \Delta W = +20J$
50J of heat is taken out of the system as the heat is lost. So, it will be negative.
$\Delta Q = -50J$
Now the total energy will be given as $\Delta U=\Delta Q+\Delta W$= -50 + 20 = -30J
Therefore the energy $\Delta E$ = -30J
So, the correct answer is “Option B”.

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.