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Chapter 7: Problem 56

What is the change in internal energy of a system if the surroundings (a) transfer 235 J of heat and 128 J of work to the system; (b) absorb 145 J of heat from the system while doing \(98 \mathrm{J}\) of work on the system; (c) exchange no heat, but receive 1.07 kJ of work from the system?

Short Answer

Expert verified
The change in internal energy for the system is (a) 107 J, (b) -243 J, (c) 1070 J

Step by step solution

01

Calculate the change in internal energy for part (a)

For part (a), both heat (Q=235 J) and work (W=128 J) are being transferred to the system. We simply replace those values into the formula: \(ΔU = Q - W\) so it results in \(ΔU = 235 - 128 = 107 J\).
02

Calculate the change in internal energy for part (b)

For part (b), the surroundings are absorbing heat from the system (Q=-145 J) and doing work on it (W=98 J). Plug these values into the equation. However, be sure to make the heat value negative, as it is being taken away from the system: \(ΔU = -145 -98 = -243 J\).
03

Calculate the change in internal energy for part (c)

For part (c), there is no exchange of heat (Q=0) and the system is doing work (W=-1.07 kJ or -1070 J as we need to convert kJ into J). Plugging these values into our formula we get: \(ΔU = 0 - (-1070) = 1070 J\).

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Most popular questions from this chapter

A 1.103 g sample of a gaseous carbon-hydrogenoxygen compound that occupies a volume of \(582 \mathrm{mL}\) at 765.5 Torr and \(25.00^{\circ} \mathrm{C}\) is burned in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) in a bomb calorimeter. The products of the combustion are \(2.108 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}), 1.294 \mathrm{g} \mathrm{H}_{2} \mathrm{O}(1),\) and enough heat to raise the temperature of the calorimeter assembly from 25.00 to \(31.94^{\circ} \mathrm{C}\). The heat capacity of the calorimeter is \(5.015 \mathrm{kJ} /^{\circ} \mathrm{C}\). Write an equation for the combustion reaction, and indicate \(\Delta H^{\circ}\) for this reaction at \(25.00^{\circ} \mathrm{C}\).

When one mole of sodium carbonate decahydrate (washing soda) is gently warmed, \(155.3 \mathrm{kJ}\) of heat is absorbed, water vapor is formed, and sodium carbonate heptahydrate remains. On more vigorous heating, the heptahydrate absorbs \(320.1 \mathrm{kJ}\) of heat and loses more water vapor to give the monohydrate. Continued heating gives the anhydrous salt (soda ash) while \(57.3 \mathrm{kJ}\) of heat is absorbed. Calculate \(\Delta H\) for the conversion of one mole of washing soda into soda ash. Estimate \(\Delta U\) for this process. Why is the value of \(\Delta U\) only an estimate?

Look up the specific heat of several elements, and plot the products of the specific heats and atomic masses as a function of the atomic masses. Based on the plot, develop a hypothesis to explain the data. How could you test your hypothesis?

James Joule published his definitive work related to the first law of thermodynamics in \(1850 .\) He stated that "the quantity of heat capable of increasing the temperature of one pound of water by \(1^{\circ} \mathrm{F}\) requires for its evolution the expenditure of a mechanical force represented by the fall of 772 lb through the space of one foot." Validate this statement by relating it to information given in this text.

Several factors are involved in determining the cooking times required for foods in a microwave oven. One of these factors is specific heat. Determine the approximate time required to warm \(250 \mathrm{mL}\) of chicken broth from \(4^{\circ} \mathrm{C}\) (a typical refrigerator temperature) to \(50^{\circ} \mathrm{C}\) in a \(700 \mathrm{W}\) microwave oven. Assume that the density of chicken broth is about \(1 \mathrm{g} / \mathrm{mL}\) and that its specific heat is approximately \(4.2 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).
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