Two kilograms of oxygen fills the cylinder of a piston-cylinder assembly. The initial volume and pressure are 2 m3 and 1 bar, respectively. Heat transfer to the oxygen occurs at constant pressure until the volume is doubled. Determine the heat transfer for the process, in kJ, assuming the specific heat ratio is constant, k = 1.35. Kinetic and potential energy effects can be ignored.

Heat transfer (Q) is 521 kJ.

Explanation: In the piston-cilinder assembly, we can suppose that the oxygen act as an ideal gas, so, it can be used the General Gas Equation:

PV=RT, where:

P is pressure;

V is volume;

m is mass;

M is molar mass;

R is a constant: R = 8.314. m³bar.K⁻¹.mol⁻¹;

T is temperature;

Using this equation, find the intial temperature:

PV = RT

1.2 = .8.314..T

T = 1.924. K

To determine the final temperature, use Combined Gas Law:

= , in which, the left side of the equality is related to the initial values and the right side, to the final values.

As pressure is constant:

T =

T =

T = 3.85. K

With the temperatures, calculate the heat transfer of the process:

Q = m.k.ΔT, where:

k is heat constant

ΔT = T -

Q = m.k.ΔT

Q = 2.1.35.(3.85 - 1.92).

Q = 521 kJ

The heat transfer in the process is 521 kJ.