Question

Calculate the change in internal energy of gas which performs 150 joules of work on obtaining 15 cals of heat.

Answer 1

We have been given heat obtained and the work done. So, we can calculate the change in Internal energy by using the first law of thermodynamics. We will convert the calories of heat in joules and later use the First law of Thermodynamics, which states that energy can neither be created or destroyed but it can be converted from one form to another.

Complete step by step answer:
$\Delta U=Q-W$
Where,
$\Delta U$= the change in internal energy of a closed
Q = the heat supplied to the system
W = amount of work done (thermodynamic) by the system on its surrounding

We know that the change in internal energy can be calculated by the first law of thermodynamics for a closed system.
Therefore,
$\Delta U=Q-W$ …………………… (1)
We have been given heat in calories, so appropriate conversion is necessary
We know,
1 calorie = 4.2 joules
Therefore,
15 calories = 15 $\times$4.2 joules = 63 joules
Therefore,
We have,
Q = 63 joules and W = 150 joules
After substituting the given values in equation (1)
We get,
$\Delta U$ = 63 – 150
$\Delta U$ = -87 joules
Therefore, change in internal energy for a given system is -87 joules.

Therefore, the correct answer is -87 joules.

Additional Information:
The negative sign in internal energy means that the energy of the system has decreased. When work is done on the system W is negative, if work is done by the system W is given as positive. Similarly, if heat is given to system Q is positive and vice versa.

Note:
The first law of thermodynamics is important as it states the conservation of energy. The first law of thermodynamics was given Rudolf Clausius and Wiliam Thomson (kelvin). They also gave the second law which states the direction of flow of heat.