Question

How much heat is needed to increase the internal energy of a gas in a piston by 4,258 J if the gas does 801 J of work on the environment by expanding if the process

Answer 1

According to the First Law of Thermodynamics, the change in internal energy (ΔU) of a system is equal to the sum of the heat (Q) added to the system and the work (W) exerted over the system:

$\Delta U=Q+W$

The sign of the heat and the work is positive when energy is transferred to the system and negative when energy is transferred from the system to its surroundings.

In this case, the system is formed by a gas on a piston, which gains 4,258 Joules in internal energy and releases 801 Joules as work. Then:

$+4258J=Q-801J$

Isolate Q from the equation to find the heat needed for this process:

$\Rightarrow Q=4258J+801J=5059J$

Therefore, the amount of heat needed to increase the internal energy of a system by 4,258J if it releases 801 of work to the environment, is 5059J.