Question

A system is given 300 calories of heat and it does 600 joules of work. How much does the internal energy of the system change in this process (J = 4.18 joules/cal)
A. 654 joule
B. 156.5 joule
C. -300 joule
D. -528.2 joule

Answer 1

We use the first law of thermodynamics to solve this problem. According to First Law of Thermodynamics, the change in internal energy of a system equals the net heat added to the system minus the net work done by the system. We convert the given heat, that is 300 calories into joules by multiplying it with J (mechanical equivalent of heat) and then subtract the given work done by the system from it.
Formula used:
The first law of thermodynamics is given by the following equation:
$\Delta U=Q-W$
where, $\Delta U$is the change in Internal energy and Q is heat added and W is work done by the system.

Complete step by step solution:
Given, Q = 300 cal.
We convert this into joules as follows:
Q = $\text{300 cal}\times \text{4}\text{.18 J/cal = 1254 J}$
Now,
W = 600 Joule
Therefore, the change in internal energy of the system is calculated as:

& \Delta U=Q-W \\\ & \text{ }=1254-600 \\\ & \text{ }=654\text{ J} \\\ \end{aligned}$$ **Hence, the correct option is A.** **Note:** First law of thermodynamics tells us about the conversion of energy from one form to another but it fails to explain in which direction the energy is flowing. For direction purposes, we use the 2nd Law of thermodynamics. Also, heat can never be converted into equivalent amounts of work. This fact is not taken into consideration in the first law of thermodynamics.