121.87
K
243.73
K
121.87
K
1,013.25
J
2,533.13
J
3,546.38
J
20.7862
J/mol·K
29.1006
J/mol·K
121.87
K
243.73
K
121.87
K
1,013.25
J
2,533.13
J
3,546.38
J
20.7862
J/mol·K
29.1006
J/mol·K
The Isobaric Process Calculator analyzes thermodynamic processes that occur at constant pressure. Isobaric processes are among the most common in nature and engineering — heating water in an open container, combustion in a gas turbine at atmospheric exhaust pressure, and many chemical reactions all proceed at approximately constant pressure.
During an isobaric process, the gas is free to expand or contract while the pressure remains fixed. The work done by the gas takes the simple form $$W = P(V_2 - V_1) = P\Delta V$$. Unlike isothermal processes, both the temperature and internal energy change. The heat transferred relates to the temperature change through the molar heat capacity at constant pressure: $$Q = nC_p\Delta T$$.
The first law of thermodynamics connects these quantities: $$Q = \Delta U + W$$. For an ideal gas with heat capacity ratio $$\gamma = C_p/C_v$$, we can derive that $$C_p = \frac{\gamma R}{\gamma - 1}$$ and $$C_v = \frac{R}{\gamma - 1}$$. This calculator determines the initial and final temperatures from the ideal gas law, then computes work, heat transfer, and internal energy change.
Engineers encounter isobaric processes in the heat addition and rejection stages of the Brayton cycle (gas turbines), the boiling and condensation stages of the Rankine cycle (steam power plants), and in HVAC heating and cooling processes. Students use isobaric analysis extensively when studying thermodynamic cycles and calorimetry.
The calculator applies the ideal gas law and first-law analysis at constant pressure:
Temperatures from ideal gas law: $$T = \frac{PV}{nR}$$, so $$T_1 = \frac{PV_1}{nR}$$ and $$T_2 = \frac{PV_2}{nR}$$
Work: $$W = P(V_2 - V_1)$$
Heat capacities: $$C_v = \frac{R}{\gamma - 1}, \quad C_p = \frac{\gamma R}{\gamma - 1}$$
Internal energy change: $$\Delta U = nC_v\Delta T$$
Heat transferred: $$Q = nC_p\Delta T$$
Verification: $$Q = \Delta U + W$$ (first law of thermodynamics)
Positive work means the gas expands; positive heat means energy flows into the system. For a diatomic ideal gas ($$\gamma = 1.4$$), $$C_p = 3.5R$$ and $$C_v = 2.5R$$, so more heat is needed to raise the temperature at constant pressure than at constant volume because part of the heat goes into doing expansion work.
When $$V_2 > V_1$$, the gas expands: work is positive, temperature rises, and heat flows in. When $$V_2 < V_1$$, the gas is compressed at constant pressure: work is negative (done on the gas), temperature drops, and heat flows out. Notice that $$Q > W$$ for expansion because some heat goes into increasing the internal energy. The ratio $$W/Q = (\gamma - 1)/\gamma$$ tells you what fraction of the added heat becomes useful work — for air ($$\gamma = 1.4$$) this is about 28.6%.
Inputs
Results
1 mol of air at 101.325 kPa expands from 0.01 to 0.02 m³. Temperature doubles from ~122 K to ~244 K, with 3546 J of heat input producing 1013 J of work and 2533 J stored as internal energy.
Inputs
Results
2 mol at 500 kPa tripled in volume. Temperature rises by ~301 K, requiring 17,500 J of heat with 5000 J delivered as work.
An isobaric process is a thermodynamic process that occurs at constant pressure. The term comes from Greek: iso (equal) and baros (weight/pressure). Common examples include boiling water at atmospheric pressure, heating gas in a piston-cylinder apparatus with a fixed weight on the piston, and combustion in a gas turbine.
At constant pressure, the gas expands as it heats, doing $$PdV$$ work on the surroundings. This work requires additional energy beyond what is needed to raise the temperature. Therefore $$C_p > C_v$$, and the difference is exactly $$C_p - C_v = R$$ per mole for an ideal gas (Mayer's relation).
Since pressure is constant, the work integral simplifies to $$W = \int P\,dV = P\int dV = P(V_2 - V_1)$$. This is simply the pressure multiplied by the change in volume, which geometrically is the rectangular area under the horizontal line on a PV diagram.
The heat capacity ratio $$\gamma = C_p/C_v$$ characterizes a gas's molecular structure. Monatomic gases (He, Ar) have $$\gamma = 5/3 \approx 1.667$$, diatomic gases (N₂, O₂, air) have $$\gamma \approx 1.4$$, and polyatomic gases (CO₂, H₂O vapor) have $$\gamma \approx 1.3$$. It determines how much of the heat goes to work versus internal energy.
Isobaric heat addition and rejection are key steps in several cycles: the Brayton cycle (gas turbines) uses two isobaric processes, the Rankine cycle (steam plants) has isobaric boiling and condensation, and the Diesel cycle approximates heat addition as isobaric during the power stroke.
Yes. Charles's Law states that at constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature: $$V/T = \text{constant}$$, or equivalently $$V_1/T_1 = V_2/T_2$$. This is a direct consequence of the ideal gas law when pressure is held fixed.
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