Question

Find the change in internal energy of the system when a system absorbs 2 kcal of heat and at the same time does 500J of work.
A. 8200J
B. 7900J
C. 6400J
D. 5600J

Answer 1

We are given the amount of energy absorbed and work done. The first law of thermodynamics gives the relation that the amount of heat energy absorbed by a system is equal to the sum of change in internal energy of the system and the amount of work done by the system.

Formula used:
The first law of thermodynamics has the following expression:
$dQ = dU + dW$
Here dQ represents the amount of heat energy absorbed by the system, dU represents the change in the internal energy of the system upon absorbing the heat dQ while dW denotes the amount of work done by the system.
Also we require following relation:
$1cal = 4.18J$

Complete step by step answer:
We have studied the first law of thermodynamics which states that when a system absorbs a certain amount of heat energy then one part of this energy is used to change the internal energy of the system while the rest of heat energy is utilized in doing work on the system.
Mathematically, it can be represented by the following expression.
$dQ = dU + dW$
Here the symbols have their usual meanings.
In the question, we are given a system which absorbs 2 kcal of heat and at the same time does 500J of work. This means that we have the following parameters.
$dQ = 2kcal = 2000cal = 2000 \times 4.18 = 8360J \\\ dW = 500J \\\$
We are asked to calculate the change in the internal energy of the system which can be obtained easily by using the expression given above for the first law of thermodynamics. The internal energy is given as:
$dU = dQ - dW$
Now we will insert the known values of amount of heat energy absorbed and amount of work done. Doing so, we get
$dU = 8360 - 500 = 7860J \simeq 7900J$
This is the required answer and hence, the correct answer is option B.

Note:
1. Keep all the units in the same system to avoid getting wrong answers.
2. The first law of thermodynamics shows the conservation of energy absorbed by a system. First, internal energy is changed then rest of energy is used to do work.