Question

(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what conditions will the quantities \(q\) and \(w\) be negative numbers?

Short answer

(a) The first law of thermodynamics is represented as: \[ \Delta U = q + w \] (b) The conditions under which \(q\) and \(w\) will be negative numbers are: - For \(q\): The system must lose heat to its surroundings. - For \(w\): Work must be done on the system.

Step-by-step solution

(a) Writing the first law of thermodynamics in terms of heat and work:

The first law of thermodynamics is represented as: \[ \Delta U = q + w \] Where: - ΔU is the change in internal energy of the system - q is the heat transferred to or from the system - w is the work done by or on the system

(b) Conditions when \(q\) and \(w\) are negative:

For heat (q) and work (w) to be negative, we need to consider their sign conventions. - For heat (q): - If the system gains heat, q is positive. - If the system loses heat, q is negative. - For work (w): - If work is done by the system, w is positive. - If work is done on the system, w is negative. So, the conditions under which \(q\) and \(w\) will be negative numbers are: - For \(q\): The system must lose heat to its surroundings. - For \(w\): Work must be done on the system.