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Chapter 6: Problem 35

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 overall change in internal energy for the process is \(\Delta E_\text{total} = 144 \mathrm{J}\).

Step by step solution

01

Calculate Change in Internal Energy for the First Step

In the first step, the system absorbs 72 J of heat (\(Q_1\)) and has 35 J of work done on it (\(W_1\)). Since work is done on the system, we must use a positive sign for \(W_1\). Thus, we can calculate the change in internal energy for the first step as: $$\Delta E_1 = Q_1 - W_1 = 72 - 35 = 37 \mathrm{J}$$
02

Calculate Change in Internal Energy for the Second Step

In the second step, the system absorbs 35 J of heat (\(Q_2\)) and performs 72 J of work (\(W_2\)). Since work is done by the system, we must use a negative sign for \(W_2\). Thus, we can calculate the change in internal energy for the second step as: $$\Delta E_2 = Q_2 - W_2 = 35 - (-72) = 35 + 72 = 107 \mathrm{J}$$
03

Calculate the Overall Change in Internal Energy

Now that we have both ΔE₁ and ΔE₂, we can calculate the overall change in internal energy by combining these values: $$\Delta E_\text{total} = \Delta E_1 + \Delta E_2 = 37 + 107 = 144 \mathrm{J}$$ So, the overall change in internal energy for the process is 144 J.

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Most popular questions from this chapter

Some automobiles and buses have been equipped to burn propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) .\) Compare the amounts of energy that can be obtained per gram of \(\mathrm{C}_{3} \mathrm{H}_{8}(g)\) and per gram of gasoline, assuming that gasoline is pure octane, $\mathrm{C}_{8} \mathrm{H}_{18}(l) .\( See Example \)6.11 .$ ) Look up the boiling point of propane. What disadvantages are there to using propane instead of gasoline as a fuel?

A piston performs work of \(210 . \mathrm{L} \cdot\) atm on the surroundings, while the cylinder in which it is placed expands from \(10 . \mathrm{L}\) to 25 \(\mathrm{L}\) . At the same time, 45 \(\mathrm{J}\) of heat is transferred from the surroundings to the system. Against what pressure was the piston working?

Which of the following processes are exothermic? a. \(\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{N}(g)\) b. \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(s)\) c. \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) d. $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)$ e. \(\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}(g)\)

In a coffee-cup calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) NaOH and 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M} \mathrm{HCl}\) are mixed. Both solutions were originally at \(24.6^{\circ} \mathrm{C}\) . After the reaction, the final temperature is \(31.3^{\circ} \mathrm{C}\) . Assuming that all the solutions have a density of 1.0 \(\mathrm{g} / \mathrm{cm}^{3}\) and a specific heat capacity of \(4.18 \mathrm{J} / \mathrm{C} \cdot \mathrm{g},\) calculate the enthalpy change for the neutralization of \(\mathrm{HCl}\) by NaOH. Assume that no heat is lost to the surroundings or to the calorimeter.

A swimming pool, 10.0 \(\mathrm{m}\) by \(4.0 \mathrm{m},\) is filled with water to a depth of 3.0 \(\mathrm{m}\) at a temperature of \(20.2^{\circ} \mathrm{C}\) . How much energy is required to raise the temperature of the water to \(24.6^{\circ} \mathrm{C} ?\)
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