Skip to main content
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 80
Chapter 19, Problem 80

FIGURE CP19.80 shows a thermodynamic process followed by 0.015 mol of hydrogen. How much heat energy is transferred to the gas?

Verified step by step guidance
1
Analyze the given problem: The problem involves a thermodynamic process for 0.015 mol of hydrogen gas. To determine the heat energy transferred, we need to use the first law of thermodynamics, which states: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat energy transferred, and W is the work done by the gas.
Determine the type of thermodynamic process shown in FIGURE CP19.80 (e.g., isothermal, isobaric, isochoric, or adiabatic). Each process has specific characteristics that affect how heat energy is calculated. For example, in an isochoric process, W = 0, so Q = ΔU. In an isothermal process, ΔU = 0, so Q = W.
Calculate the work done (W) by the gas during the process. For example, if the process involves a pressure-volume change, use the formula: W = ∫ P dV. If the process is isothermal for an ideal gas, W can also be calculated using: W = nRT ln(Vf/Vi), where n is the number of moles, R is the ideal gas constant, T is the temperature, and Vf and Vi are the final and initial volumes, respectively.
Calculate the change in internal energy (ΔU) of the gas. For a diatomic gas like hydrogen, the internal energy is related to temperature by the formula: ΔU = (f/2) nRΔT, where f is the degrees of freedom (f = 5 for diatomic gases at room temperature), n is the number of moles, R is the ideal gas constant, and ΔT is the change in temperature.
Combine the results from the previous steps to solve for Q using the first law of thermodynamics: Q = ΔU + W. Substitute the values of ΔU and W into this equation to find the heat energy transferred to the gas.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
9m
Was this helpful?

Key Concepts

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

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It encompasses laws that describe how energy is transferred and transformed in physical systems. Understanding thermodynamic processes is essential for analyzing how heat energy is transferred to or from a gas, as in the case of the hydrogen mentioned in the question.
Recommended video:
Guided course
08:04
The First Law of Thermodynamics

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or system to another due to a temperature difference. It can occur through conduction, convection, or radiation. In the context of the question, calculating the heat energy transferred to the hydrogen gas requires understanding the specific process it undergoes and the conditions affecting heat exchange.
Recommended video:
Guided course
05:14
Overview of Heat Transfer

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law is crucial for determining the state of the hydrogen gas and calculating the heat energy transferred during the thermodynamic process.
Recommended video:
Guided course
07:21
Ideal Gases and the Ideal Gas Law
Related Practice
Textbook Question

10 g of aluminum at 200°C and 20 g of copper are dropped into 50 cm3 of ethyl alcohol at 15°C. The temperature quickly comes to 25°C. What was the initial temperature of the copper?

2
views
Textbook Question

In Problems 75, 76, and 77 you are given the equation used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation.

50J=−n(8.31J/mol K)(350K)ln(13)(200×10−6m3)(13,600kg/m3)50\,\(\text{J}\)=-n(8.31\,\(\text{J/mol K}\))(350\,\(\text{K}\))\(\ln\]\left\)(\(\frac\)13\(\right\))(200\(\times\)10^{-6}\,\(\text{m}\)^3)(13,600\,\(\text{kg/m}\)^3)

1
views
Textbook Question

A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of 1200°C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20°C water and dousing it. The lava has density 2500 kg/m3, specific heat 1100 J/kg K, melting temperature 800°C, and heat of fusion 4.0×105 J/kg. How many liters of water per minute, at a minimum, will be needed to save the town?

2
views