Question

In a thermodynamic process, the pressure of a fixed mass of a gas is changed such that the gas releases 20 J of heat and 8 J of work is done on the gas. If the initial internal energy of the gas was 30 J, then what will the final energy be?

• A. 2J
• B. 58J
• C. 18J
• D. 42J

Answer 1

The correct option is C

18J

Explanation for the correct option:

Option (C):

• As per the given data:
• The heat released in the process, $\mathrm{dQ}=-20\mathrm{J}$
• Work done on the system, $\mathrm{dW}=-8\mathrm{J}$
• And the initial internal energy of the process,${\mathrm{U}}_1=30\mathrm{J}$
• According to the 1st law of thermodynamics:

$$\begin{gathered} \mathrm{dQ}=\mathrm{dU}+\mathrm{dW} \\ \Rightarrow \mathrm{dU}=\mathrm{dQ}-\mathrm{dW} \\ =-20+8 \\ =-12\mathrm{J} \end{gathered}$$

• Hence, the final internal energy of the process can be calculated as:

$$\begin{gathered} \mathrm{U}2=\mathrm{U}1+\mathrm{dU} \\ =30-12 \\ =18\mathrm{J} \end{gathered}$$

Therefore, the final energy of the system has been calculated to be 18J.