Question

A gas absorbs \(45 \mathrm{~kJ}\) of heat and does \(29 \mathrm{~kJ}\) of work. Calculate \(\Delta E\).

Short answer

The change in internal energy, ΔE, of the gas is \(16 \mathrm{~kJ}\).

Step-by-step solution

Recall the first law of thermodynamics

The first law of thermodynamics is given by the formula: \[ \Delta E = q - w \] where ΔE is the change in internal energy, q is the heat absorbed by the system, and w is the work done by the system.

Substitute given values into the formula

We are given the heat absorbed (q) as 45 kJ and the work done (w) as 29 kJ. Substitute these values into the formula: \[ \Delta E = 45 \mathrm{~kJ} - 29 \mathrm{~kJ} \]

Calculate the change in internal energy

Now, perform the subtraction to find the change in internal energy: \[ \Delta E = 16 \mathrm{~kJ} \] The change in internal energy, ΔE, of the gas is 16 kJ.