Question

Calculate \(\Delta E\) for each of the following. a. \(q=-47 \mathrm{kJ}, w=+88 \mathrm{kJ}\) b. \(q=+82 \mathrm{kJ}, w=-47 \mathrm{kJ}\) c. \(q=+47 \mathrm{kJ}, w=0\) d. In which of these cases do the surroundings do work on the system?

Short answer

The calculated values for \(\Delta E\) are: a. \(\Delta E = 41 \mathrm{kJ}\) b. \(\Delta E = 35 \mathrm{kJ}\) c. \(\Delta E = 47 \mathrm{kJ}\) The surroundings do work on the system in case a.

Step-by-step solution

Case a: \(q=-47 \mathrm{kJ}, w=+88 \mathrm{kJ}\)

Given \(q = -47 \mathrm{kJ}\) and \(w = 88 \mathrm{kJ}\), we can calculate \(\Delta E\) using the formula: \[\Delta E = q + w = -47 + 88\] Now solve for \(\Delta E\): \[\Delta E = 41 \mathrm{kJ}\]

Case b: \(q=+82 \mathrm{kJ}, w=-47 \mathrm{kJ}\)

Given \(q = 82 \mathrm{kJ}\) and \(w = -47 \mathrm{kJ}\), we can calculate \(\Delta E\) using the formula: \[\Delta E = q + w = 82 - 47\] Now solve for \(\Delta E\): \[\Delta E = 35 \mathrm{kJ}\]

Case c: \(q=+47 \mathrm{kJ}, w=0\)

Given \(q = 47 \mathrm{kJ}\) and \(w = 0\), we can calculate \(\Delta E\) using the formula: \[\Delta E = q + w = 47 + 0\] Now solve for \(\Delta E\): \[\Delta E = 47 \mathrm{kJ}\]

Identifying cases where surroundings do work on the system

To determine in which cases the surroundings do work on the system, we need to analyze the sign of the \(w\) values. If \(w\) is positive, that means the surroundings are doing work on the system, and if \(w\) is negative, the system is doing work on the surroundings. - Case a: \(w = +88 \mathrm{kJ}\), surroundings do work on the system. - Case b: \(w = -47 \mathrm{kJ}\), system does work on the surroundings. - Case c: \(w = 0\), no work is done. So, in case a, the surroundings do work on the system.