Ideal-Gas Specific Internal Energy Change
Calculate a mass-specific property change from temperature change and a constant heat capacity.
Try this formula
Calculate change in mass-specific internal energy or choose another supported quantity.
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Try this formula
Calculate change in mass-specific internal energy or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Change in mass-specific internal energy
Enter the known values to see the result.
Use an ideal gas with the stated specific heat approximately constant over the temperature interval. Use a mass-specific heat capacity for a result in J/kg. For an ideal gas, this property change depends on temperature alone; the actual path need not have constant volume. Heat transferred is not generally equal to this property change; account for work and flow terms separately.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra and introductory thermodynamics
Source
Teng-Jui Lin — CHEM E 326 — Chemical Engineering ThermodynamicsReference equation: Measurable properties — Constant volume heat capacity. FormuLab wrote new explanations, assumptions, applications, and numerical examples. Integrated the ideal-gas property derivative with constant mass-specific heat capacity; did not equate property change with process heat.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Integrated the ideal-gas property derivative with constant mass-specific heat capacity; did not equate property change with process heat.
Definition
An ideal gas’s internal energy depends only on temperature. With a constant mass-specific heat capacity, integrating its temperature derivative gives a property change proportional to the temperature difference.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Change in mass-specific internal energy | ||
| Mass-specific heat capacity at constant volume | ||
| Final absolute temperature | ||
| Initial absolute temperature |
Real-World Applications
Gas property changes
Estimate an ideal-gas property difference.
Energy balances
Supply a property change while treating process heat and work separately.
Worked Example
Problem
An ideal gas has cv = 718 J/(kg·K) and warms from 300 K to 400 K. Find its specific property change.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Measurable properties — Constant volume heat capacity. FormuLab wrote new explanations, assumptions, applications, and numerical examples. Integrated the ideal-gas property derivative with constant mass-specific heat capacity; did not equate property change with process heat.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Integrated the ideal-gas property derivative with constant mass-specific heat capacity; did not equate property change with process heat.
Assumptions
- • Use an ideal gas with the stated specific heat approximately constant over the temperature interval.
- • Use a mass-specific heat capacity for a result in J/kg.
- • For an ideal gas, this property change depends on temperature alone; the actual path need not have constant volume.
- • Heat transferred is not generally equal to this property change; account for work and flow terms separately.
Languages
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