Explanation 1) Concept: By using the molar specific heat at constant volume and pressure and substituting these values in the formula for heat and change in internal energy, we can calculate the energy transferred to the gas as heat and change in internal energy of gas. Using the first law of thermodynamics , we can find the work done by the gas. 2) Formulae: i) Q = n C P Δ T ii) Δ E i n t = n C V Δ T iii) W = Q - Δ E i n t iv) Δ K t r a n s = Δ n K a v g v) Δ E i n t = Δ K t r a n s + Δ K r o t 3) Given: i) Number of moles n = 3 m o l ii) Temperature is T = 40 ℃ 4) Calculations: a) Energy transferred to the gas as heat: For a diatomic gas, C V = 5 2 R and as C P = C V + R , C P = 5 2 R + R C P = 7 2 R The molar specific heat C P is C P = Q n Δ T Q = n C P Δ T where Q is the energy transferred as heat to or from a sample of n mole of the gas, Δ T is the resulting change in temperature of the gas, and Δ E i n t is the change in the internal energy of the gas. Substituting all values in the above equation, we get Q = 3 × 7 2 R × Δ T Q = 3 × 7 2 × 8.31 × 40 Q = 3.49 × 10 3 J b) Change in internal energy of gas: The molar specific heat C V of a gas at constant volume is given as C V = Q n Δ T = Δ E i n t n Δ T Thus, Δ E i n t = n C V Δ T Also, C V = 5 2 R Substituting this in the equation for internal energy, we get Δ E i n t = n × 5 2 R × 40 Δ E i n t = 3 × 5 2 × 8

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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First law of Thermodynamics

The word thermodynamics consists of two words: thermo- and dynamics. Dynamics means the study of motion. The field of thermodynamics is all about the study of the movement of heat. In a more meaningful way, it is stated as the study of the transfer of en…

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Chapter 19, Problem 43P

To determine

To find:

a) Energy transferred to the gas as heat.

b) Change in internal energy of the gas.

c) Work done by the gas.

d) Increase in the rotational kinetic energy of the gas.

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Chapter 19, Problem 42P

Chapter 19, Problem 44P

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Chapter 19 Solutions

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a) Energy transferred to the gas as heat. b) Change in internal energy of the gas. c) Work done by the gas. d) Increase in the rotational kinetic energy of the gas.

Solution Summary: The author calculates the energy transferred to the gas as heat and change in internal energy using the first law of thermodynamics.

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To find: a) Energy transferred to the gas as heat. b) Change in internal energy of the gas. c) Work done by the gas. d) Increase in the rotational kinetic energy of the gas.

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Chapter 19 Solutions

To find:

a) Energy transferred to the gas as heat.

b) Change in internal energy of the gas.

c) Work done by the gas.

d) Increase in the rotational kinetic energy of the gas.