20.7
First Law Of Thermodynamics: Problem-Solving
The first law of thermodynamics states that the change in internal energy of the system is equal to the net heat transfer into the system minus the ne…
The first law of thermodynamics states that the heat added to a system is utilized in performing the work and increasing the system's internal energy.
Consider an example where 100 grams of water at one atmospheric pressure converts into steam at 100 degrees Celsius. What is the change in the internal energy for this thermodynamic process?
This thermodynamic system changes from the initial liquid to the final gaseous state at constant temperature and pressure when water converts to steam.
The heat transfer into the system is the product of mass and the latent heat of the vaporization of water.
The work done is equal to the product of pressure and volume change. Using the value of mass and density of the steam and water, the volume change and so the work done is estimated.
Here the unknown quantity is the change in the internal energy, while the known quantities are heat supplied and work done by the system. So, applying the first law of thermodynamics, a change in internal energy can be estimated.
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Q1: How do you apply the first law of thermodynamics to solve problems?
Identify the thermodynamic system and list its initial and final states. Determine which quantities are known and unknown, ensuring consistent units throughout. Apply the first law equation: change in internal energy equals heat added minus work done by the system. Substitute known values to calculate the unknown quantity, considering sign conventions where positive heat enters the system and positive work is done by it.
Q2: What is the relationship between heat, work, and internal energy change?
The first law of thermodynamics states that the change in internal energy equals net heat transfer into the system minus net work done by the system. This equation represents energy conservation: heat supplied either increases the system's internal energy or performs work. The relationship applies to any thermodynamic process regardless of the path taken between initial and final states.
Q3: Why is sign convention important when using the first law of thermodynamics?
Sign convention determines whether quantities increase or decrease the system's internal energy. Heat is positive when added to the system and negative when removed. Work is positive when done by the system and negative when done on the system. Applying incorrect signs produces wrong results, so carefully tracking polarity of both heat and work is essential for accurate calculations.
Q4: How is work calculated when a system undergoes volume change?
Work done by a system during volume change equals pressure multiplied by the change in volume. For constant pressure processes, this calculation is straightforward. Using the mass, density, and latent heat values, you can determine volume changes for phase transitions like water converting to steam, then calculate work done during volume expansion.
Q5: What does it mean that internal energy change is path independent?
Internal energy change depends only on initial and final states, not on the specific path taken between them. This property allows you to calculate internal energy change for any process if you know the initial and final state values. Regardless of whether a system follows different routes or processes, the change in internal energy remains constant.
Q6: How do you calculate internal energy change for a phase transition like vaporization?
For a phase transition at constant temperature and pressure, calculate heat transfer using mass times latent heat of vaporization. Determine work done from pressure times volume change between liquid and gas phases. Apply the first law equation to find internal energy change by subtracting work done from heat supplied to the system.
Q7: What unit consistency is required when solving first law problems?
All quantities must use compatible units to ensure correct results. If pressure is in Pascals and volume in cubic meters, work must be expressed in Joules. Verify that heat, work, and internal energy all use the same energy unit system. Inconsistent units lead to calculation errors and incorrect internal energy values.