Question

Show that the work done by an ideal gas during an isothermal change of state (from initial state 1 to final state 2), in a closed container is given by; 1W2=m.R.T(ln(v2/v1))

A piston-cylinder device contains 0.2 kg of air, initially at
27oC and 100 kPa. The air is then slowly compressed in an
**isothermal** process to a final pressure of 400 kPa.
Determine: (a) The work done during this process, and
(b) The heat transferred.

Answer #1

In a cylinder/piston arrangement, air is compressed in a
reversible polytropic process to a final state of 800 kPa, 500 K.
Initially air is at 110 kPa and 25oC. During the
compression process heat transfer takes place with the ambient
maintained at 25oC. Assume air as an ideal gas (R =0.287
kJ/kg) and has constant specific heats of Cp = 1.004
kJ/kgK and Cv = 0.717 kJ/kgK. If the mass of air in the
cylinder is 0.1286 kg, determine
a)...

A cylinder of monatomic ideal gas is sealed in a cylinder by a
piston. Initially, the gas occupies a volume of 3.00 L and the
pressure is initially 105 kPa. The cylinder is placed in an oven
that maintains the temperature at a constant value. 65.0 J of work
is then done on the piston, compressing the gas (in other words,
the gas does −65.0 J of work). The work is done very slowly so that
the gas maintains a...

0.5 kilograms of air are compressed from 100 kPa and 300 K in a
polytropic process, n = 1.3, to a state where V2 = 0.5
V1. The air is further compressed at constant pressure
until the final volume is 0.2 V1 . Draw a sketch of the
processes on a p-V diagram. Determine the work for each
process.

Two moles of nitrogen are initially at 10 bar and 600 K (state
1) in a horizontal piston/cylinder device. They are expanded
adiabatically to 1 bar (state 2). They are then heated at constant
volume to 600 K (state 3). Finally, they are isothermally returned
to state 1. Assume that N 2 is an ideal gas with a constant heat
capacity as given on the back flap of the book. Neglect the heat
capacity of the piston/cylinder device. Suppose that...

A 0.2 m3 piston-cylinder initially contains 400 K air. A heavy
frictionless piston maintains a pressure of 500 kPa abs. Then, a
weakness in the cylinder wall blows out and creates a hole. Air
escapes through the hole until the piston drops far enough to cover
the hole. At that point, the volume is half the initial volume.
During this process, 75 kJ of heat is transferred to the 100 kPa,
300 K surroundings. Using Cp = 1.005 kJ/kg-K and...

1-kg water in a frictionless piston-cylinder device is initially
at 250°C and 300 kPa (state
1). A total of 700 kJ of work is done ON the water
in order to isothermally reduce its volume to
1/20 of its initial volume (state 2). Determine the magnitude and
direction of the heat transfer
involved in this process.
Answer: -1147 kJ.

A cylinder sealed with a piston contains an ideal gas. Heat is
added to the gas while the piston remains locked in place until the
absolute temperature of the gas doubles.
1. The pressure of the gas a. doubles b. stays the same c. drops
in half
2. The work done by the surroundings on the gas is a. positive
b. negative c. zero
3. The thermal energy of the gas a. doubles b. stays the same c.
drops in...

Air expands in a polytropic process (n = 1.35) from 2 MPa and
1200 K to 150 kPa in a piston/cylinder. Determine per
unit mass of air the work produced and the heat transferred during
the expansion process in kJ/kg.

A heat engine composed of 1.6 moles of an ideal, monotonic gas
is initially at 350 K and 1x10^5 Pa. The first step is an
isothermal expansion to a pressure of 5x10^4 Pa. Second, the gas is
compressed at constant pressure back to the inital volume. Finally
the gas returns, at constant volume to the initial state. What is
the total work done by the gas during this cycle? What is the
efficiency of this cycle?

A gas initially at 2.8 bar and 60ºC is compressed to a final
pressure of 14 bar in an isothermal internally reversible process.
Determine the work and heat transfer, each in kJ per kg of gas, if
the gas is (a) Refrigerant 134a, (b) air as an ideal gas. Sketch
the process on p–v and T–s coordinates

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