500 J of heat energy are transferred to a gas during a process in which the gas expands at constant pressure from 400 cm3 to 800 cm3. The gas's thermal energy increases by 300 J during this process. What is the gas pressure?

Ch 19: Work, Heat, and the First Law of Thermodynamics

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 19: Work, Heat, and the First Law of Thermodynamics

Problem 11

Chapter 19, Problem 11

500 J of heat energy are transferred to a gas during a process in which the gas expands at constant pressure from 400 cm³ to 800 cm³. The gas's thermal energy increases by 300 J during this process. What is the gas pressure?

Verified step by step guidance

Step 1: Understand the problem. The gas undergoes a process where heat energy is transferred, and it expands at constant pressure. The thermal energy change and the work done by the gas are related to the heat energy transferred. We need to calculate the pressure of the gas.

Step 2: Recall the first law of thermodynamics: \( Q = \Delta U + W \), where \( Q \) is the heat energy transferred, \( \Delta U \) is the change in thermal energy, and \( W \) is the work done by the gas. Substitute the given values: \( Q = 500 \; \text{J} \) and \( \Delta U = 300 \; \text{J} \).

Step 3: Calculate the work done by the gas using \( W = Q - \Delta U \). Substitute \( Q = 500 \; \text{J} \) and \( \Delta U = 300 \; \text{J} \) into the equation to find \( W \).

Step 4: Recall the formula for work done by a gas at constant pressure: \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume. Convert the volume from \( \text{cm}^3 \) to \( \text{m}^3 \) (since \( 1 \; \text{cm}^3 = 10^{-6} \; \text{m}^3 \)) and calculate \( \Delta V = V_{\text{final}} - V_{\text{initial}} \).

Step 5: Rearrange the formula \( W = P \Delta V \) to solve for \( P \): \( P = \frac{W}{\Delta V} \). Substitute the values of \( W \) and \( \Delta V \) into the equation to find the pressure of the gas.

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Key Concepts

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

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 thermodynamic processes, it relates the change in internal energy of a system to the heat added to the system and the work done by the system. This principle is crucial for analyzing energy transfers in processes involving gases.

Work Done by a Gas

When a gas expands at constant pressure, the work done by the gas can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume. This work represents the energy transferred as the gas pushes against external pressure during expansion. Understanding this concept is essential for determining the pressure of the gas in the given scenario.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas, where n is the number of moles and R is the ideal gas constant. This law is fundamental in thermodynamics and allows for the calculation of pressure when the volume and temperature of a gas are known. In this problem, it can be used to find the pressure after determining the work done and the change in internal energy.