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Chapter 6: Problem 31

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

Short Answer

Expert verified
The heat transferred to the thermodynamic system is \(375\,\text{J}\).

Step by step solution

01

Write down the equation for the first law of thermodynamics.

The first law of thermodynamics equation can be written as: \[ \Delta U = Q - W \] Where: - \(\Delta U\) is the change in internal energy. - \(Q\) is the amount of heat transferred. - \(W\) is the work done.
02

Substitute the given values into the equation.

We are given the values for the internal energy increase (\(\Delta U = 300\,\text{J}\)) and the expansion work done (\(W = 75\,\text{J}\)). Plugging these values into the equation, we get: \[ 300\,\text{J} = Q - 75\,\text{J} \]
03

Solve for the heat transferred.

To find the amount of heat transferred (\(Q\)), we need to isolate \(Q\) in our equation. We do this by adding \(75\,\text{J}\) to both sides of the equation: \[ 300\,\text{J} + 75\,\text{J} = Q \] Now, we simply add the values on the left side: \[ 375\,\text{J} = Q \]
04

Determine the direction of the heat transfer.

Since the value of \(Q\) is positive (\(375\,\text{J}\)), it means that the heat was transferred to the system. If the value of \(Q\) were negative, then it would have meant that the heat was transferred from the system. So, the heat transferred to the thermodynamic system is \(375\,\text{J}\).

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Most popular questions from this chapter

Nitromethane, \(\mathrm{CH}_{3} \mathrm{NO}_{2}\), can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly $$ \mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ a. The standard enthalpy change of reaction \(\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)\) for the balanced reaction (with lowest whole- number coefficients) is \(-1288.5 \mathrm{~kJ} .\) Calculate the \(\Delta H_{\mathrm{f}}^{\circ}\) for nitromethane. b. A \(15.0\) - \(\mathrm{L}\) flask containing a sample of nitromethane is filled with \(\mathrm{O}_{2}\) and the flask is heated to \(100 .^{\circ} \mathrm{C}\). At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen ( \(\chi_{\text {nitrogen }}\) ) is \(0.134\) after the reaction is complete, what mass of nitrogen was produced?

For the following reactions at constant pressure, predict if \(\Delta H>\) \(\Delta E, \Delta H<\Delta E\), or \(\Delta H=\Delta E\) a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Consider the reaction $$ \begin{array}{r} 2 \mathrm{HCl}(a q)+\mathrm{Ba}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{BaCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H=-118 \mathrm{~kJ} \end{array} $$ Calculate the heat when \(100.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{HCl}\) is mixed with \(300.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\). Assuming that the temperature of both solutions was initially \(25.0^{\circ} \mathrm{C}\) and that the final mixture has a mass of \(400.0 \mathrm{~g}\) and a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\), calculate the final temperature of the mixture.

The enthalpy of combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) when \(\mathrm{H}_{2} \mathrm{O}(l)\) is formed is \(-891 \mathrm{~kJ} / \mathrm{mol}\) and the enthalpy of combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) when \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is formed is \(-803 \mathrm{~kJ} / \mathrm{mol} .\) Use these data and Hess's law to determine the enthalpy of vaporization for water.

Combustion of table sugar produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) When \(1.46 \mathrm{~g}\) table sugar is combusted in a constant-volume (bomb) calorimeter, \(24.00 \mathrm{~kJ}\) of heat is liberated. a. Assuming that table sugar is pure sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\), write the balanced equation for the combustion reaction. b. Calculate \(\Delta E\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose. c. Calculate \(\Delta I I\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose at \(25^{\circ} \mathrm{C}\).
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