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Chapter 5: Problem 31

During a normal breath, our lungs expand about 0.50 L against an external pressure of 1.0 atm. How much work is involved in this process (in J)?

Short Answer

Expert verified
The work involved in this process is approximately -50.66 J (in Joules).

Step by step solution

01

Convert volume to SI units

We are given the volume expansion in liters (L) and need to convert it to cubic meters (m³) which is the SI unit for volume. To do so, we will use the conversion factor: 1 L = 0.001 m³ \newline \(\Delta V\) = 0.50 L \newline \(0.50 L \times \frac{0.001 m³}{1 L} \) \newline \(\Delta V = 0.0005 m³\)
02

Convert pressure to SI units

We are given the pressure in atmospheres (atm) and need to convert it to pascals (Pa) which is the SI unit for pressure. To do so, we will use the conversion factor: 1 atm = 101325 Pa \newline \(P =\) 1.0 atm \newline \(1.0 atm \times \frac{101325 Pa}{1 atm}\) \newline \(P = 101325 Pa\)
03

Calculate the work done

Now that we have the volume and pressure in SI units, we can apply the formula for calculating the work done against a constant external pressure: \newline \(W = -P \Delta V\) \newline Substituting the values, we get: \newline \(W = -(101325 Pa)(0.0005 m³)\) \newline \(W = -50.6625 J\) Since the work done is negative, it means that the work is done by the body to expand the lungs. Therefore, the work involved in this process is approximately -50.66 J (in Joules).

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Most popular questions from this chapter

When a 6.50 -g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18\()\) the temperature rises from 21.6 to to \(37.8^{\circ} \mathrm{C}\) . (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} )\) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

In a thermodynamic study, a scientist focuses on the properties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the apparatus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? (b) If the inlet and outlet were closed, what type of system would it be?

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Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to \(\operatorname{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g),(\mathbf{c})\) the work accomplished in burning a gallon of gasoline.

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) 1 \(\mathrm{mol} \mathrm{CO}_{2}(s)\) or 1 \(\mathrm{mol} \mathrm{CO}_{2}(g)\) at the same temperature, ( b) 2 \(\mathrm{mol}\) of hydrogen atoms or 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2},(\mathbf{c}) 1 \mathrm{mol} \mathrm{H}_{2}(g)\) and 0.5 \(\mathrm{mol} \mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) or 1 \(\mathrm{mol} \mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C},(\mathbf{d}) 1 \mathrm{mol} \mathrm{N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\) or 1 \(\mathrm{mol} \mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) .
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