Question

Ідеальний газ при тиску 0,5 МПа (P1)і об'ємі (V1) 100 см^3 ізобарно розширюється, при цьому його температура змінюється від t1 20 C до t2 500C. Потім його тиск ізотермічно зменшується у два рази. Знайти об'єм газу при цьому тиску. Нарисувати графік цих процесів в осях (P, V).

Answer 1

Ideal Gas Process Calculation and Graph

To solve this problem, we can use the ideal gas law equation, which states that for a given amount of gas, the pressure times the volume is proportional to the temperature. The equation is expressed as:

P1V1 / T1 = P2V2 / T2

Where: - P1 = initial pressure - V1 = initial volume - T1 = initial temperature - P2 = final pressure - V2 = final volume - T2 = final temperature

First, we can calculate the final volume of the gas after the isobaric expansion and the isothermal compression. Then, we can plot the processes on a (P, V) graph.

Calculating Final Volume after Isobaric Expansion

The initial conditions are: - Initial pressure (P1) = 0.5 MPa = 0.5 * 10^6 Pa - Initial volume (V1) = 100 cm^3 = 100 * 10^-6 m^3 - Initial temperature (t1) = 20°C = 293.15 K (using the conversion t(K) = t(°C) + 273.15)

The final temperature (t2) = 50°C = 773.15 K

Using the ideal gas law equation, we can calculate the final volume (V2) after the isobaric expansion.

P1V1 / T1 = P2V2 / T2

V2 = (P1V1 * T2) / (P2 * T1)

Let's calculate the final volume (V2) using the given values.

Calculating Volume after Isothermal Compression

After the isobaric expansion, the pressure is isothermally reduced by half. We can calculate the final volume (V3) after this process.

P2V2 = P3V3

V3 = 2 * V2

Now, we have the final volume (V3) after the isothermal compression.

Plotting the Processes on a (P, V) Graph

We can plot the processes on a (P, V) graph to visualize the changes in pressure and volume during the isobaric expansion and isothermal compression.

Let's calculate the final volume (V2) and (V3) and then plot the processes on the graph.