Question

What is the change in internal energy of a system if the surroundings (a) transfer 235 J of heat and 128 J of work to the system; (b) absorb 145 J of heat from the system while doing \(98 \mathrm{J}\) of work on the system; (c) exchange no heat, but receive 1.07 kJ of work from the system?

Short answer

The change in internal energy for the system is (a) 107 J, (b) -243 J, (c) 1070 J

Step-by-step solution

Calculate the change in internal energy for part (a)

For part (a), both heat (Q=235 J) and work (W=128 J) are being transferred to the system. We simply replace those values into the formula: \(ΔU = Q - W\) so it results in \(ΔU = 235 - 128 = 107 J\).

Calculate the change in internal energy for part (b)

For part (b), the surroundings are absorbing heat from the system (Q=-145 J) and doing work on it (W=98 J). Plug these values into the equation. However, be sure to make the heat value negative, as it is being taken away from the system: \(ΔU = -145 -98 = -243 J\).

Calculate the change in internal energy for part (c)

For part (c), there is no exchange of heat (Q=0) and the system is doing work (W=-1.07 kJ or -1070 J as we need to convert kJ into J). Plugging these values into our formula we get: \(ΔU = 0 - (-1070) = 1070 J\).

Key concepts

First Law of Thermodynamics

In the realm of thermodynamics, understanding how energy flows within a system and its surroundings is governed by the First Law of Thermodynamics. It's a fundamental principle stating that energy cannot be created or destroyed, but merely transformed from one form to another.
In practical terms, this means that the change in internal energy of a system ( ΔU = Q - W ) can be calculated by accounting for the heat added to the system ( Q ) and the work done by the system ( W ).
In our original exercise, this principle provides clarity: simply plug in the values of heat and work to determine how the system's internal energy is altered.

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object or system to another. This can occur in several forms such as conduction, convection, and radiation.
In the context of thermodynamics, we focus on how much heat energy ( Q ) is added to or removed from a system.
- If heat energy is added (positive Q ), the internal energy typically increases. - If heat energy is removed (negative Q ), the internal energy decreases.
In part (b) of the original solution, for instance, the system loses heat while part (a) gains it, illustrating how heat transfer directly impacts the total internal energy of a system.

Work in Thermodynamics

Work in thermodynamics refers to the energy transferred when an external force moves a boundary of the system.
This is captured in the formula for internal energy change as work done on or by the system ( W ).
The sign of W can vary:

• If work is done on the system, W is positive.
• If work is done by the system, W is negative.

In the exercise's part (c), note that no heat is exchanged but the system performs work on the surroundings, resulting in a negative W value that significantly alters internal energy.