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Chapter 15: Problem 8

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

Expert verified
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

01

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: $$Q = -W$$
02

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: $$W = 5.00 \times 1000 = 5000 \mathrm{J}$$
03

Calculate the heat transfer

Using the equation we derived in Step 1, we can now calculate the heat transfer as: $$Q = -W$$ $$Q = -5000 \mathrm{J}$$
04

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.

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Most popular questions from this chapter

A heat engine takes in \(125 \mathrm{kJ}\) of heat from a reservoir at $815 \mathrm{K}\( and exhausts \)82 \mathrm{kJ}\( to a reservoir at \)293 \mathrm{K}$ (a) What is the efficiency of the engine? (b) What is the efficiency of an ideal engine operating between the same two reservoirs?
Show that in a reversible engine the amount of heat \(Q_{C}\) exhausted to the cold reservoir is related to the net work done \(W_{\text {net }}\) by $$ Q_{\mathrm{C}}=\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}-T_{\mathrm{C}}} W_{\mathrm{net}} $$
An electric power station generates steam at \(500.0^{\circ} \mathrm{C}\) and condenses it with river water at \(27^{\circ} \mathrm{C} .\) By how much would its theoretical maximum efficiency decrease if it had to switch to cooling towers that condense the steam at \(47^{\circ} \mathrm{C} ?\)
On a cold day, Ming rubs her hands together to warm them up. She presses her hands together with a force of \(5.0 \mathrm{N} .\) Each time she rubs them back and forth they move a distance of \(16 \mathrm{cm}\) with a coefficient of kinetic friction of \(0.45 .\) Assuming no heat flow to the surroundings, after she has rubbed her hands back and forth eight times, by how much has the internal energy of her hands increased?

On a cold winter day, the outside temperature is \(-15.0^{\circ} \mathrm{C} .\) Inside the house the temperature is \(+20.0^{\circ} \mathrm{C}\) Heat flows out of the house through a window at a rate of \(220.0 \mathrm{W}\). At what rate is the entropy of the universe changing due to this heat conduction through the window?
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