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Chapter 6: Problem 32

A system undergoes a process consisting of the following two steps: Step \(1:\) The system absorbs \(72 \mathrm{~J}\) of heat while \(35 \mathrm{~J}\) of work is done on it. Step 2: The system absorbs \(35 \mathrm{~J}\) of heat while performing \(72 \mathrm{~J}\) of work. Calculate \(\Delta E\) for the overall process.

Short Answer

Expert verified
The change in internal energy for the overall process, ΔE, can be calculated by adding the change in internal energy for each step: ΔE1 = 107 J and ΔE2 = -37 J. Therefore, ΔE_overall = ΔE1 + ΔE2 = 107 J + (-37 J) = \(70 \mathrm{~J}\).

Step by step solution

01

Calculate heat and work for Step 1 of the process

In Step 1, we are given that the system absorbs 72 J of heat and 35 J of work is done on it. Since work is being done on the system, it has a negative value. So, we have: Q1 = 72 J W1 = -35 J
02

Calculate heat and work for Step 2 of the process

In Step 2, the system absorbs 35 J of heat and performs 72 J of work. Since work is being done by the system, it has a positive value. So, we have: Q2 = 35 J W2 = 72 J
03

Calculate ΔE for each step using the first law of thermodynamics

Using the first law of thermodynamics, ΔE = Q - W, calculate the change in internal energy for each step: ΔE1 = Q1 - W1 = 72 J - (-35 J) = 72 J + 35 J = 107 J ΔE2 = Q2 - W2 = 35 J - 72 J = -37 J
04

Calculate ΔE for the overall process by adding the results of each step

Now, add the change in internal energy for each step to find the change in internal energy for the overall process: ΔE_overall = ΔE1 + ΔE2 = 107 J + (-37 J) = 70 J The change in internal energy for the overall process is 70 J.

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Most popular questions from this chapter

In a coffee-cup calorimeter, \(1.60 \mathrm{~g} \mathrm{NH}_{4} \mathrm{NO}_{3}\) is mixed with \(75.0 \mathrm{~g}\) water at an initial temperature of \(25.00^{\circ} \mathrm{C}\). After dissolution of the salt, the final temperature of the calorimeter contents is \(23.34^{\circ} \mathrm{C}\). Assuming the solution has a heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in units of \(\mathrm{kJ} / \mathrm{mol}\).

A \(5.00-\mathrm{g}\) sample of aluminum pellets (specific heat capacity \(=\) \(0.89 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) and a \(10.00-\mathrm{g}\) sample of iron pellets (specific heat capacity \(=0.45 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) are heated to \(100.0^{\circ} \mathrm{C}\). The mixture of hot iron and aluminum is then dropped into \(97.3 \mathrm{~g}\) water at \(22.0^{\circ} \mathrm{C}\). Calculate the final temperature of the metal and water mixture, assuming no heat loss to the surroundings.

A \(30.0\) -g sample of water at \(280 . \mathrm{K}\) is mixed with \(50.0 \mathrm{~g}\) water at \(330 . \mathrm{K}\). Calculate the final temperature of the mixture assuming no heat loss to the surroundings.

Consider the substances in Table 6.1. Which substance requires the largest amount of energy to raise the temperature of \(25.0 \mathrm{~g}\) of the substance from \(15.0^{\circ} \mathrm{C}\) to \(37.0^{\circ} \mathrm{C} ?\) Calculate the energy. Which substance in Table \(6.1\) has the largest temperature change when \(550 . \mathrm{g}\) of the substance absorbs \(10.7 \mathrm{~kJ}\) of energy? Calculate the temperature change.

The overall reaction in a commercial heat pack can be represented as $$ 4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{~kJ} $$ a. How much heat is released when \(4.00\) moles of iron are reacted with excess \(\mathrm{O}_{2}\) ? b. How much heat is released when \(1.00\) mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{~g}\) iron is reacted with excess \(\mathrm{O}_{2}\) ? d. How much heat is released when \(10.0 \mathrm{~g} \mathrm{Fe}\) and \(2.00 \mathrm{~g} \mathrm{O}_{2}\) are reacted?
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