Question

An ideal gas is in contact with a heat reservoir so that it remains at a constant temperature of \(300.0 \mathrm{K}\). The gas is compressed from a volume of \(24.0 \mathrm{L}\) to a volume of 14.0 L. During the process, the mechanical device pushing the piston to compress the gas is found to expend \(5.00 \mathrm{kJ}\) of energy. How much heat flows between the heat reservoir and the gas and in what direction does the heat flow occur?

Short answer

Answer: The heat transfer between the gas and the heat reservoir is -5000 J, and the direction of the heat flow is from the gas into the heat reservoir.

Step-by-step solution

Write the First Law of Thermodynamics equation for the given problem

Since we know that the change in internal energy (\(\Delta U\)) is zero, we can rewrite the First Law of Thermodynamics equation as: $$Q = -W$$

Convert the work done into Joules

We are given the work done by the mechanical device as \(5.00 \mathrm{kJ}\). To be consistent with the units, we need to convert this value into Joules. We know that \(1 \mathrm{kJ} = 1000 \mathrm{J}\), so the work done is: $$W = 5.00 \times 1000 = 5000 \mathrm{J}$$

Calculate the heat transfer

Using the equation we derived in Step 1, we can now calculate the heat transfer as: $$Q = -W$$ $$Q = -5000 \mathrm{J}$$

Determine the direction of heat flow

Since the calculated heat transfer (\(Q\)) is negative, this means that the heat is flowing out of the gas and into the heat reservoir. In conclusion, the heat flows between the heat reservoir and the gas is \(-5000 \mathrm{J}\), and the direction of the heat flow is from the gas into the heat reservoir.