Question

A gas is compressed at constant pressure 50 $ N/{{m}^{2}} $ from a volume of $ 10{{m}^{3}} $ to a volume $ 4{{m}^{3}} $ . Energy 100 J is then added to the gas by heating. Its internal energy is

• A. increased by 100 J
• B. increased by 200 J
• C. decreased by 200 J
• D. increased by 400 J

Answer 1

Answer: (D)

Change in volume $ \Delta {{V}_{2}}-{{V}_{1}}=4-10=-6\,{{m}^{3}} $
A volume decreases, work is done on the gas and so it is negative.
$ W=p\Delta V=50\times (-6) $
$ =-300J $
Additional heat supplied
$ (G=+100\text{ }J) $ .
So, for first law of thermodynamics change in external energy is given by
$ \Delta U=Q-W $
$ =100-(-300)=400\text{ }J $
Internal energy increases by 400 J.