Question

Find the external work done by the system in $kcal$ , when $20{\text{ }}kcal$ of heat of heat is supplied to the system and the increase in the internal energy is $8400{\text{ }}J$ ($J{\text{ }} = {\text{ }}4200{\text{ }}J/kcal$) ?

Answer 1

We are given here with heat supplied and work done and thus we will use the concept of the first law of thermodynamics. Then, we will substitute the suitable values. Finally, we will perform suitable conversions wherever necessary and answer the question in the required unit.

Formula used:
$Q{\text{ }} = {\text{ }}W{\text{ }} + {\text{ }}\Delta U$
Where, $Q$ is the heat supplied on the system, $W$ is the work done by the system and $\Delta U$ is the change in internal energy of the system.

Complete step by step answer:
We first note down the given values for our convenience,
Given, change in internal energy is
$\Delta U{\text{ }} = {\text{ }}8400{\text{ }}J$
Heat supplied,
$Q{\text{ }} = {\text{ }}20{\text{ }}kcal{\text{ }} \Rightarrow Q{\text{ }}= {\text{ }}20{\text{ }} \times {\text{ }}4200{\text{ }} \Rightarrow Q{\text{ }}= {\text{ }}84000{\text{ }}J$

Now, we know from the equation of the first law of thermodynamics,
$Q{\text{ }} = {\text{ }}W{\text{ }} + {\text{ }}\Delta U$
Further, we get
$W{\text{ }} = {\text{ }}Q{\text{ }} - {\text{ }}\Delta U$
Putting in the given values, we get
$W{\text{ }} = {\text{ }}84000{\text{ }} - {\text{ }}8400{\text{ }} \\\ \Rightarrow W{\text{ }}= {\text{ }}75600{\text{ }}J$
For conversion, we will divide this value by the conversion ratio
$W{\text{ }} = {\text{ }}\dfrac{{75600}}{{4200}}{\text{ }} \\\ \therefore W{\text{ }}= {\text{ }}18{\text{ }}kcal$

Hence, $18{\text{ }}kcal$ amount of work is done by the system.

Note: Students often commit errors while using the conversion value which means whether to multiply or to divide. A wrong step can lead to a very absurd answer practically. Thus, students should be very much cautious during the conversion part as there are high chances of committing blunders. Students should also be careful while using the values in the equation of the first law of thermodynamics and the meaning of the parameters involved in it as students commit errors while substituting as they misunderstand the meaning of the parameters of the formula. So they have to be highly concerned while performing the above mentioned step as this step plays a very vital role in the evaluation process.