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Chapter 15: Problem 40

In a certain chemical process, a lab technician supplies \(254 \mathrm{~J}\) of heat to a system. At the same time, \(73 \mathrm{~J}\) of work are done on the system by its surroundings. What is the increase in the internal energy of the system?

Short Answer

Expert verified
The increase in internal energy is 327 J.

Step by step solution

01

Understanding the First Law of Thermodynamics

The first law of thermodynamics can be expressed as \( \Delta U = Q + W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done on the system. Here, we have \( Q = 254 \mathrm{~J} \) and \( W = 73 \mathrm{~J} \).
02

Substituting Values into the Formula

Using the formula \( \Delta U = Q + W \), substitute \( Q = 254 \mathrm{~J} \) and \( W = 73 \mathrm{~J} \) to find the change in internal energy: \( \Delta U = 254 + 73 \).
03

Calculating the Change in Internal Energy

Add the values to determine the increase in internal energy: \( \Delta U = 254 + 73 = 327 \mathrm{~J} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Internal Energy
Internal energy is a central concept in thermodynamics, representing the total energy contained within a system. It includes all microscopic forms of energy, such as kinetic and potential energies of molecules. When we talk about a change in internal energy, it's about measuring how the system's energy state has shifted.
If you add heat to a system or do work on it, its internal energy will increase. Conversely, removing heat or having work done by the system reduces its internal energy. In our exercise, the internal energy increased by 327 J due to added heat and work done on it.
Remember, internal energy is an intrinsic property. It's not directly observable, but its changes are, through temperature shifts or work outputs.
Heat Transfer
Heat transfer is the flow of thermal energy from one object or substance to another. It occurs due to a temperature difference and moves spontaneously from hotter to cooler areas, seeking balance.
The First Law of Thermodynamics highlights the impact of heat transfer. It states that the heat added to a system (\( Q \)) contributes to the change in the system's internal energy. In our example, 254 J of heat were provided to increase the internal energy.
  • Important to note: The sign of \( Q \) matters. Positive \( Q \) indicates heat added to the system, while negative \( Q \) shows heat removed.
This understanding helps predict how systems evolve when subjected to heat changes.
Work Done
Work done in thermodynamics refers to the energy transfer associated with forces applied over distances. Work can increase or decrease a system's internal energy.
Within the First Law of Thermodynamics, the work done on a system (\( W \)) is added to the internal energy equation. In our case, 73 J of work were done on the system, aiding in the increase of its internal energy.
  • Similar to heat transfer, the sign of \( W \) matters: Positive \( W \) indicates work done on the system, while negative \( W \) implies work done by the system.
Understanding work done helps grasp how energy is transferred through forces and motion.
Chemical Processes
Chemical processes often involve complex interactions where energy plays a crucial role. These processes can cause changes in the internal energy of a system as reactants transform into products.
In the context of our exercise, the chemical process was imbued with energy through heat and work. This resulted in a measurable change in internal energy, following the First Law of Thermodynamics.
  • Energy input (heat added or work done) can drive reactions forward, breaking and forming bonds.
  • The amount of energy change gives insight into the reaction's spontaneity and potential.
Grasping how energy changes in chemical processes aids in predicting reaction behaviors and understanding thermodynamic laws.

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Most popular questions from this chapter

The gas inside a balloon will always have a pressure nearly equal to atmospheric pressure, since that is the pressure applied to the outside of the balloon. You fill a balloon with helium (a nearly ideal gas) to a volume of \(0.600 \mathrm{~L}\) at a temperature of \(19.0^{\circ} \mathrm{C}\). What is the volume of the balloon if you cool it to the boiling point of liquid nitrogen \((77.3 \mathrm{~K}) ?\)

One way to improve insulation in windows is to fill a sealed space between two glass panes with a gas that has a lower thermal conductivity than that of air. The thermal conductivity \(k\) of a gas depends on its molar heat capacity \(C_{V},\) molar mass \(M,\) and molecular radius \(r\). The dependence on those quantities at a given temperature is approximately \(k \propto C_{V} / r^{2} \sqrt{M}\). The noble gases have properties that make them particularly good choices as insulating gases. Noble gases range from helium (molar mass \(4.0 \mathrm{~g} / \mathrm{mol}\), molecular radius \(0.13 \mathrm{nm}\) ) to xenon (molar mass \(131 \mathrm{~g} / \mathrm{mol}\), molecular radius \(0.22 \mathrm{nm}\) ). (The noble gas radon is heavier than xenon, but radon is radioactive and so is not suitable for this purpose.) Give one reason why the noble gases are preferable to air (which is mostly nitrogen and oxygen) as an insulating material. A. Noble gases are monatomic, so no rotational modes contribute to their molar heat capacity. B. Noble gases are monatomic, so they have lower molecular masses than do nitrogen and oxygen. C. The molecular radii in noble gases are much larger than those of gases that consist of diatomic molecules. D. Because noble gases are monatomic, they have many more degrees of freedom than do diatomic molecules, and their molar heat capacity is reduced by the number of degrees of freedom.

(a) How much heat does it take to increase the temperature of 2.50 moles of an ideal monatomic gas from \(25.0^{\circ} \mathrm{C}\) to \(55.0^{\circ} \mathrm{C}\) if the gas is held at constant volume? (b) How much heat is needed if the gas is diatomic rather than monatomic? (c) Sketch a \(p V\) diagram for these processes.

A cylinder with a piston contains \(0.250 \mathrm{~mol}\) of ideal oxygen at a pressure of \(2.40 \times 10^{5} \mathrm{~Pa}\) and a temperature of \(355 \mathrm{~K}\). The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a \(p V\) diagram. (b) Compute the temperature during the isothermal compression. (c) Compute the maximum pressure. (d) Compute the total work done by the piston on the gas during the series of processes.

A \(20.0 \mathrm{~L}\) tank contains \(0.225 \mathrm{~kg}\) of helium at \(18.0^{\circ} \mathrm{C}\). The molar mass of helium is \(4.00 \mathrm{~g} / \mathrm{mol}\). (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in pascals and in atmospheres?
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