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Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblem 57d
Chapter 19, Problem 57d

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What amount of heat energy is transferred from the gas as its pressure decreases?

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Step 1: Identify the type of thermodynamic process. The problem states that the process is isobaric, meaning the pressure remains constant throughout the expansion. This simplifies the analysis as we can use the formula for heat transfer in an isobaric process: Q = nCpΔT.
Step 2: Calculate the number of moles of nitrogen gas. Use the ideal gas law, PV = nRT, to find the number of moles (n). Rearrange the equation to solve for n: n = (P × V) / (R × T). Substitute the given values: P = 3.0 atm, T = 20°C (convert to Kelvin: T = 20 + 273 = 293 K), and use the gas constant R = 0.0821 L·atm/(mol·K). Note that the initial volume is not provided directly, but it will cancel out later in the calculation.
Step 3: Determine the change in temperature (ΔT). Since the volume triples during the expansion, the final temperature can be calculated using the ideal gas law, assuming pressure remains constant. The relationship between temperature and volume in an isobaric process is T_final / T_initial = V_final / V_initial. Given that V_final = 3 × V_initial, T_final = 3 × T_initial. Therefore, ΔT = T_final - T_initial = (3 × 293 K) - 293 K.
Step 4: Use the molar specific heat capacity at constant pressure (Cp) for nitrogen gas. Nitrogen is a diatomic molecule, so Cp = (7/2)R, where R = 8.314 J/(mol·K) in SI units. Calculate Cp and substitute it into the formula for heat transfer: Q = nCpΔT.
Step 5: Combine all the values to express the heat transfer (Q). Substitute n (from Step 2), Cp (from Step 4), and ΔT (from Step 3) into the formula Q = nCpΔT. This will give the amount of heat energy transferred during the isobaric expansion. Note that the sign of Q will indicate whether heat is absorbed or released by the gas.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isobaric Process

An isobaric process is a thermodynamic process in which the pressure remains constant while the volume and temperature of the gas change. During this type of expansion, the gas does work on its surroundings, and heat must be added or removed to maintain the constant pressure. Understanding this concept is crucial for analyzing how heat energy is transferred during the expansion of the gas.
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First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of an isobaric process, the change in internal energy of the gas is equal to the heat added to the system minus the work done by the system. This principle helps in calculating the heat energy transferred during the expansion of the gas.
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Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or system to another due to a temperature difference. In the case of the nitrogen gas undergoing isobaric expansion, heat is transferred from the gas to the surroundings as its pressure decreases. Understanding the mechanisms of heat transfer, including conduction, convection, and radiation, is essential for determining the amount of energy exchanged.
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Related Practice
Textbook Question

0.10 mol of nitrogen gas follow the two processes shown in FIGURE P19.58. How much heat is required for each?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. How much heat energy is transferred to the gas to cause this expansion?

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Textbook Question

Two cylinders each contain 0.10 mol of a diatomic gas at 300 K and a pressure of 3.0 atm. Cylinder A expands isothermally and cylinder B expands adiabatically until the pressure of each is 1.0 atm. What are the final temperature and volume of each?

Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What are the gas volume and temperature after the expansion?

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Textbook Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What is the gas pressure after the decrease?

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Textbook Question

FIGURE P19.62 shows a thermodynamic process followed by 120 mg of helium. How much work is done on the gas during each of the three segments?

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