Question

A Carnot engine woolsho 377°c and 37°c produces 120x10^8j of
work determine the following quantities (1) thermal efficinay
of engine . (2) heat rejected. (3) entropy changed during the
process.
​

Answer 1

Answer:

We can see how entropy is defined by recalling our discussion of the Carnot engine. We noted that for a Carnot cycle, and hence for any reversible processes,

QcQh=TcTh" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 17.44px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 4.446em; min-height: 0px; width: 10000em; position: relative;">QcQh=TcThQcQh=TcTh.

Rearranging terms yields

QcTc=QhTh" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 17.44px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 4.573em; min-height: 0px; width: 10000em; position: relative;">QcTc=QhThQcTc=QhTh

for any reversible process. Qc and Qh are absolute values of the heat transfer at temperatures Tc and Th, respectively. This ratio of QT" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 17.44px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0.941em; min-height: 0px; width: 10000em; position: relative;">QTQT is defined to be the change in entropy ΔS for a reversible process, ΔS=(QT)rev" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 17.44px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 5.946em; min-height: 0px; width: 10000em; position: relative;">ΔS=(QT)revΔS=(QT)rev, where Q is the heat transfer, which is positive for heat transfer into and negative for heat transfer out of, and T is the absolute temperature at which the reversible process takes place. The SI unit for entropy is joules per kelvin (J/K). If temperature changes during the process, then it is usually a good approximation (for small changes in temperature) to take T to be the average temperature, avoiding the need to use integral calculus to find ΔS.

The definition of ΔS is strictly valid only for reversible processes, such as used in a Carnot engine. However, we can find ΔS precisely even for real, irreversible processes. The reason is that the entropy S of a system, like internal energy U, depends only on the state of the system and not how it reached that condition. Entropy is a property of state. Thus the change in entropy ΔS of a system between state 1 and state 2 is the same no matter how the change occurs. We just need to find or imagine a reversible process that takes us from state 1 to state 2 and calculate ΔS for that process. That will be the change in entropy for any process going from state 1 to state 2. (See Figure 2.)

Explanation:

see the figures

Figure 2. When a system goes from state 1 to state 2, its entropy changes by the same amount ΔS, whether a hypothetical reversible path is followed or a real irreversible path is taken.