Piston Problem for Engineering Thermodynamics

[cathy88]

Homework Statement

Problem shown in attach picture

A cylinder of total internal volume 0.10 m3 has a
frictionless internal piston (of negligible mass and
thickness) which separates 0.50 kg of water below
the piston from air above it. Initially the water exists
as saturated liquid at 120°C and the air, also at
120°C, exerts a pressure such that it exactly
balances the upward force exerted by the water.
(refer to the figure right). Heat is then transferred into
the entire cylinder, such that the two substances are
at the same temperature at any instant, until a final
State 2 having a uniform temperature of 180°C is
reached. The air may be assumed to behave ideally,
having R = 0.287 kJ kg-1
K-1; cp0 = 1.004 kJ kg-1
K-1;
cv0 = 0.717 kJ kg-1
K-1.
(a) What is the mass of air in the cylinder?
(b) Determine both the volume below the piston, and the dryness fraction of
the water occupying that volume when State 2 is reached.
(c) What is the change in the total internal energy of:
(i) the air; and
(ii) the water
during the entire heat addition process from State 1 to State 2.
(d) How much heat has been transferred into the complete system comprising
both water and air?

Homework Equations

I really have no idea, I was trying with pV=mRT

The Attempt at a Solution

Im totally stuned by this question, I tried doing pV=mRT but that was wrong the a) is 0.175kg. COuld someone please help me how I could start going through this problem?

Thanks

 

[bucher]

In order to do the PV = mRT, you'll need to know the pressure and the volume (temperature is known). The pressure can be found using a water table (you probably have one). It's a table showing all of the pressures, densities, and other information at certain temperatures.
You'll find the volume of the air this way as well since you'll probably find the density of the water in the table.

 

[Mene]

for providing the problem statement and your attempt at a solution. This is a classic piston problem in engineering thermodynamics, which involves the principles of ideal gas law, specific heat capacities, and energy conservation. Let's break down the problem into smaller steps and see if we can solve it together.

Step 1: Determine the initial state of the system (State 1)

The initial state of the system is when the water exists as saturated liquid at 120°C and the air also at 120°C. We know that the pressure of the air is balancing the upward force exerted by the water, which means the pressure of the air is equal to the saturation pressure of water at 120°C. We can use the steam tables to find this pressure, which is 2.338 bar. This also means that the air is in a saturated state at 120°C.

Step 2: Calculate the mass of air in the cylinder (a)

To calculate the mass of air, we can use the ideal gas law, which is pV = mRT. We know the pressure (2.338 bar), volume (0.10 m3), and temperature (120°C = 393.15 K) of the air at State 1. We also know the gas constant (R = 0.287 kJ/kg-K). Plugging in these values, we get:

(2.338 bar)(0.10 m3) = m(0.287 kJ/kg-K)(393.15 K)

Solving for m, we get m = 0.175 kg. This is the mass of air in the cylinder.

Step 3: Determine the final state of the system (State 2)

The final state of the system is when the entire cylinder is at a uniform temperature of 180°C. This means that both the water and air will reach this temperature at State 2.

Step 4: Calculate the volume below the piston and the dryness fraction of water (b)

To determine the volume below the piston, we can use the ideal gas law again. We know the pressure (2.338 bar), mass of air (0.175 kg), and temperature (180°C = 453.15 K) at State 2. This time, we also know the gas constant for air (R = 0.287 kJ/kg-K). Plugging in these values, we get:

(2.338 bar)(V) = (