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Chapter 6: Problem 29

A gas absorbs \(45 \mathrm{~kJ}\) of heat and does \(29 \mathrm{~kJ}\) of work. Calculate \(\Delta E\).

Short Answer

Expert verified
The change in internal energy, \(\Delta E = 16 \, \mathrm{kJ}\).

Step by step solution

01

Write down the given values

We are given the following values: - \(q = 45 \,\mathrm{kJ}\) (heat absorbed by the gas) - \(w = -29 \,\mathrm{kJ}\) (work done by the gas; we use a negative sign since work is done by the system)
02

Apply the first law of thermodynamics

According to the first law of thermodynamics, the change in internal energy of a system can be calculated by using the formula: \[\Delta E = q + w\] We can plug in the values of \(q\) and \(w\): \[\Delta E = 45 \,\mathrm{kJ} - 29 \,\mathrm{kJ}\]
03

Solve for \(\Delta E\)

Now, we just need to perform the subtraction: \[\Delta E = 16 \,\mathrm{kJ}\] The change in internal energy, \(\Delta E\), is 16 kJ.

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Most popular questions from this chapter

If the internal energy of a thermodynamic system is increased by \(300 . \mathrm{J}\) while \(75 \mathrm{~J}\) of expansion work is done, how much heat was transferred and in which direction, to or from the system?

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.

Which of the following substances have an enthalpy of formation equal to zero? a. \(\mathrm{Cl}_{2}(g)\) b. \(\mathrm{H}_{2}(g)\) c. \(\mathrm{N}_{2}(l)\) d. \(\mathrm{Cl}(g)\)

Consider the following reaction: \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-891 \mathrm{~kJ}\) Calculate the enthalpy change for each of the following cases: a. \(1.00 \mathrm{~g}\) methane is burned in excess oxygen. b. \(1.00 \times 10^{3} \mathrm{~L}\) methane gas at 740 . torr and \(25^{\circ} \mathrm{C}\) are burned in excess oxygen.

At \(298 \mathrm{~K}\), the standard enthalpies of formation for \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\) are \(227 \mathrm{~kJ} / \mathrm{mol}\) and \(49 \mathrm{~kJ} / \mathrm{mol}\), respectively. a. Calculate \(\Delta H^{\circ}\) for $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) $$ b. Both acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) can be used as fuels. Which compound would liberate more energy per gram when combusted in air?
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