Solution Found!
Applying the Entropy Balance: Closed SystemsThe
Chapter 6, Problem 77P(choose chapter or problem)
The temperature of an incompressible substance of mass m and specific heat c is reduced from \(T_{0}\) to \(T\left(<T_{0}\right)\) by a refrigeration cycle. The cycle receives energy by heat transfer at T from the substance and discharges energy by heat transfer at \(T_{0}\) to the surroundings. There are no other heat transfers. Plot \(\left(W_{\min } / m c T_{0}\right)\) versus \(T / T_{0}\) ranging from 0.8 to 1.0, where Wmin is the minimum theoretical work input required.
Questions & Answers
QUESTION:
The temperature of an incompressible substance of mass m and specific heat c is reduced from \(T_{0}\) to \(T\left(<T_{0}\right)\) by a refrigeration cycle. The cycle receives energy by heat transfer at T from the substance and discharges energy by heat transfer at \(T_{0}\) to the surroundings. There are no other heat transfers. Plot \(\left(W_{\min } / m c T_{0}\right)\) versus \(T / T_{0}\) ranging from 0.8 to 1.0, where Wmin is the minimum theoretical work input required.
ANSWER:Step 1 of 3
We have to determine the minimum theoretical work input required in reducing the temperature of an incompressible substance of mass m and specific heat c is reduced from to T (<
) by a refrigeration cycle.
The energy balance equation for the above process is given by
Where,
is the change in the energy an incompressible substance
is work input
Now, the change in internal energy is given by the equation
is mass of the substance
is specific heat of the substance
Thus,
The work input equation is