If the internal energy of a thermodynamic system is decreased by 300 J when 75 J of work is done on the system, how much heat was transferred, and in which direction, to or from the system?
To determine the amount of heat transferred and the direction of heat transfer, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat transferred (Q) into the system minus the work done (W) by the system. Mathematically, this can be represented as:
ΔU = Q - W
Given that the internal energy (ΔU) of the system decreased by 300 J and the work done (W) on the system is 75 J, we can substitute these values into the equation:
-300 J = Q - 75 J
To isolate the variable Q, we can rearrange the equation:
Q = -300 J + 75 J
Q = -225 J
The amount of heat transferred (Q) is -225 J, indicating that 225 J of heat was transferred out of the system. The negative sign signifies that heat was lost by the system.
To determine the amount of heat transferred into or out of the system, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
The equation is:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat transferred, and W is the work done.
Given that the change in internal energy (ΔU) is -300 J (decreased), and the work done (W) is +75 J (done on the system), we can substitute these values into the equation:
-300 J = Q - 75 J
Now, let's isolate Q, the unknown heat transferred:
Q = -300 J + 75 J
Q = -225 J
The negative sign indicates that 225 J of heat was transferred from the system.
delta E = q+w
work on the system is +
q out is -
q in is +