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Chapter 15: 15-2Q (page 412)
Can mechanical energy ever be transformed completely into heat or internal energy? Can the reverse happen? In each case, if your answer is no, explain why not, if yes, give one or two examples.
Mechanical energy can be transformed completely into heat, and the reverse can also happen.
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(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand isothermally back to its original volume. Draw the process on a PV diagram.
Question: (III) The PV diagram in Fig. 15鈥�23 shows two possible states of a system containing 1.75 moles of a monatomic ideal gas. \(\left( {{P_1} = {P_2} = {\bf{425}}\;{{\bf{N}} \mathord{\left/{\vphantom {{\bf{N}} {{{\bf{m}}^{\bf{2}}}}}} \right.} {{{\bf{m}}^{\bf{2}}}}},\;{V_1} = {\bf{2}}{\bf{.00}}\;{{\bf{m}}^{\bf{3}}},\;{V_2} = {\bf{8}}{\bf{.00}}\;{{\bf{m}}^{\bf{3}}}.} \right)\) (a) Draw the process which depicts an isobaric expansion from state 1 to state 2, and label this process A. (b) Find the work done by the gas and the change in internal energy of the gas in process A. (c) Draw the two-step process which depicts an isothermal expansion from state 1 to the volume \({V_2}\), followed by an isovolumetric increase in temperature to state 2, and label this process B. (d) Find the change in internal energy of the gas for the two-step process B.
If \({\bf{1}}{\bf{.00}}\;{{\bf{m}}{\bf{3}}}\) of water at 0掳C is frozen and cooled to \( - {\bf{8}}{\bf{.}}{{\bf{0}}{\bf{o}}}{\bf{C}}\) by being in contact with a great deal of ice at \( - {\bf{8}}{\bf{.}}{{\bf{0}}{\bf{o}}}{\bf{C}}\) estimate the total change in entropy of the process.
Question: (II) The pressure in an ideal gas is cut in half slowly, while being kept in a container with rigid walls. In the process, 465 kJ of heat left the gas. (a) How much work was done during this process? (b) What was the change in internal energy of the gas during this process?
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