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Question: What is the internal energy change when $X$ J of work is done on the system and $Y$ J of heat is t...

What is the internal energy change when

XX J of work is done on the system and

YY J of heat is transferred to surrounding?

A

X+YX + Y ]

B

XYXY }

C

Y−XY-X J

D

X−YX - Y J

Answer

X - Y J

Explanation

Solution

Using the first law of thermodynamics:

ΔU=Q−W\Delta U = Q - W

Here,

  • Work done on the system =X= X J implies work done by the system =−X= -X J.
  • Heat transferred to the surroundings means the system loses heat, so Q=−YQ = -Y J.

Substitute into the equation:

ΔU=(−Y)−(−X)=X−YJ\Delta U = (-Y) - (-X) = X - Y \quad \text{J}