Problem $5(10$ points$)-$ Energy Balance with Water and $P-v$ diagram

A piston$-$cylinder assembly contains water as shown on the right. Stops are

located within the cylinder such that the piston cannot lower past the stops.

There is $0\mathrm{.}2$ kg of water in the assembly at an initial pressure of $1\mathrm{.}2$ MPa and

an initial temperature of $400$ Celsius. You may assume that changes in kinetic

and potential energy in this problem are negligible. The piston$-$cylinder

assembly goes through a $2-$step process:

Process $1-2$ : The water goes through a constant$-$pressure cooling process

until the piston contacts the stops. The volume in State $2$ is half of the volume

in State $1.$

Process $2-3$: While the piston remains in contact with the stops, the water

goes throrgh a constant$-$volume cooling process until the water cools to $100$

degrees Celsius.

A$.$ Calculate the boundary work done in Process $1-2$ in kJ$.$ Indicate the work as a positive number

that is either $"$in$"$ or "out." Note that the boundary work $(W_{1-2})$ can be calculated as:

$W_{\text{o}\text{u}\text{t}\text{,}1-2}={\displaystyle \underset{1}{\overset{2}{}}}PdV$

Where $P$ is pressure and $V$ is volume. Note that because this is a constant$-$pressure process, the

mathematical evaluation of this integral is straightforward.

B$.$ Determine the heat associated with Process $1-2(Q_{1-2})$ in kJ$.$ Indicate the heat as a positive number

that is either $"$in$"$ or "out".

C$.$ Determine the heat associated with Process $2-3(Q_{2-3})$ in kJ$.$ Indicate the heat as a positive number

trfat is either $"$in$"$ or "out".

D$.$ Sketch the processes in series on a P$-$v diagram. This sketch does not need to be drawn to scale.

However, it does need correctly illustrate the state locations and processes in a qualitative

manner. The sketch should also include the $2-$phase dome and the isotherms curves

corresponding to States $1,2,$ and $3.$

Problem $5(10$ points$)-$ Energy Balance with Water and $P-v$ diagram

A piston$-$cylinder assembly contains water as shown on the right. Stops are

located within the cylinder such that the piston cannot lower past the stops.

There is $0\mathrm{.}2$ kg of water in the assembly at an initial pressure of $1\mathrm{.}2$ MPa and

an initial temperature of $400$ Celsius. You may assume that changes in kinetic

and potential energy in this problem are negligible. The piston$-$cylinder

assembly goes through a $2-$step process:

Process $1-2$ : The water goes through a constant$-$pressure cooling process

until the piston contacts the stops. The volume in State $2$ is half of the volume

in State $1.$

Process $2-3$: While the piston remains in contact with the stops, the water

goes through a constant$-$volume cooling process until the water cools to $100$

degrees Celsius.

Problem $5(10$ points$)-$ Energy Balance with Water and $P-v$ diagram

A piston$-$cylinder assembly contains water as shown on the right. Stops are

located within the cylinder such that the piston cannot lower past the stops.

There is $0\mathrm{.}2$ kg of water in the assembly at an initial pressure of $1\mathrm{.}2$ MPa and

an initial temperature of $400$ Celsius. You may assume that changes in kinetic

and potential energy in this problem are negligible. The piston$-$cylinder

assembly goes through a $2-$step process:

Process $1-2$ : The water goes through a constant$-$pressure cooling process

until the piston contacts the stops. The volume in State $2$ is half of the volume

in State $1.$

Process $2-3$: While the piston remains in contact with the stops, the water

goes through a constant$-$volume cooling process until the water cools to $100$

degrees Celsius.

A$.$ Calculate the boundary work done in Process $1-2$ in kJ$.$ Indicate the work as a positive number

that is either $"$in$"$ or "out." Note that the boundary work $(W_{1-2})$ can be calculated as:

$W_{\text{o}\text{u}\text{t},1-2}={\displaystyle \underset{1}{\overset{2}{}}}PdV$

Where $P$ is pressure and $V$ is volume. Note that because this is a constant$-$pressure process, the

mathematical evaluation of this integral is straightforward.

B$.$ Determine the heat associated with Process $1-2(Q_{1-2})$ in kJ $.$ Indicate the heat as a positive number

that is either $"$in$"$ or "out".

C$.$ Determine the heat associated with Process $2-3(Q_{2-3})$ in kJ $.$ Indicate the heat as a positive number

thlat is either $"$in$"$ or "out".

D$.$ Sketch the processes in series on a P$-$v diagram. This sketch does not need to be drawn to scale.

However, it does need correctly illustrate the state locations and processes in a qualitative

manner. The sketch should also include the $2-$phase dome and the isotherms curves

corresponding to States $1,2,$ and $3.$

A$.$ Calculate