METU, ChE 204
May 13, 2014
Thermodynamics I, Section 06
Prof. Dr. Tülay Özbelge
Asst. Emine Kayahan
HOMEWORK-9
(Date Due: May 20, 2014)
Solve these problems to study, but submit only Problems 3, 4, 6 and 7.
1) An ideal vapor-compression refrigeration cycle with a capacity of 3 tons has R-134a entering
the compressor as saturated vapor at − 20C and exiting at 1MPa.
a) Determine the coefficient of performance of the cycle,
b) Determine the power input to the compressor.
2) A vapor-compression refrigeration cycle using R-134a has evaporator and condenser
pressures of 201.7 kPa and 1MPa, respectively. The isentropic efficiency of the turbine is 0.85.
Calculate the coefficient of performance.
3) A heat pump which operates on an ideal vapor-compression cycle with refrigerant-12 is used
to heat water from 15C to 54C at a rate of 0.18 kg/s. The condenser and evaporator pressures
are 1.4 and 0.32 MPa, respectively. Determine the power input to the heat pump.
4) Koretsky, 2nd ed, problem 3.62) Consider a refrigeration system based on an ideal vaporcompression cycle using R – 134a as the refrigerant. It operates between 0.7 MPa and 0.12 MPa
with a flow rate of 0.5 mol/s. Calculate the following:
a. the rate of heat removal from the refrigerant unit
b. the power input needed to the compressor
c. the COP
The properties of R-134a can be found at http://webbook.nist.gov/chemistry/fluid/ or use the
distributed data sheets.
5) An automobile air conditioner uses a vapor compression refrigeration cycle with
environmentally friendly refrigerant HFC-134a as the working fluid. The following data are
available for this cycle.
Point
1
2
3
4
Fluid state
Saturated liquid
Vapor – liquid mixture
Saturated vapor
Superheated vapor
Temperature
55⁰C
5⁰C
a. Supply the missing temperatures, pressures, enthalpies and entropies for this cycle.
b. Evaluate the coefficient of performance for the refrigeration cycle described in this
problem.
6) By measuring the temperature of change and the specific volume change accompanying a
small pressure change in a reversible adiabatic process, one can evaluate the derivative
𝜕𝑇
( )
𝜕𝑃 𝑠
and the adiabatic compressibility
𝐾𝑠 = −
1 𝜕𝑣
( )
𝑣 𝜕𝑃 𝑠
Develop an expression for (𝜕𝑇⁄𝜕𝑃 )𝑠 in terms of T, v, Cp, α, and KT and show that
𝐾𝑠
𝐶𝑣
=
𝐾𝑇
𝐶𝑝
7) Prove that the following statements are true.
a. (𝜕𝐻⁄𝜕𝑣) 𝑇 is equal to zero if (𝜕𝐻⁄𝜕𝑃) 𝑇 is equal to zero.
b. The derivative of (𝜕𝑆⁄𝜕𝑣)𝑃 for a fluid has the same sign as its coefficient of thermal
expansion α and is inversely proportional to it.