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Chapter 15: Q1P (page 412)

(I) An ideal gas expands isothermally, performing\({\bf{4}}{\bf{.30 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{J}}\) of work in the process. Calculate (a) the change in internal energy of the gas, and (b) the heat absorbed during this expansion.

Short Answer

Expert verified

(a) The change in internal energy is zero.

(b) The heat absorbed in the system is \(4.30 \times {10^3}\;{\rm{J}}\).

Step by step solution

01

Concepts

From the first law of thermodynamics,\(\Delta U = Q - W\).

For the isothermal process, the change in internal energy is\(\Delta U = 0\).

02

Given data

The work done in the process is \(W = 4.30 \times {10^3}\;{\rm{J}}\).

03

Calculation 

Part (a)

For the isothermal process, the change in internal energy is zero.

Part (b)

For the isothermal process,

\(\begin{array}{c}0 = Q - W\\Q = W\\Q = 4.30 \times {10^3}\;{\rm{J}}{\rm{.}}\end{array}\)

Hence, the absorbed heat in the system is \(4.30 \times {10^3}\;{\rm{J}}\).

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Most popular questions from this chapter

Question: (II) (a) What is the coefficient of performance of an ideal heat pump that extracts heat from 6°C air outside and deposits heat inside a house at 24°C? (b) If this heat pump operates on 1200 W of electrical power, what is the maximum heat it can deliver into the house each hour? See Problem 35.

A “Carnot” refrigerator (the reverse of a Carnot engine) absorbs heat from the freezer compartment at a temperature of -17°C and exhausts it into the room at 25°C.

(a) How much work would the refrigerator do to change 0.65 kg of water at 25°C into ice at -17°C.

(b) If the compressor output is 105 W and runs 25% of the time, how long will this take?

Question: (II) A heat pump is used to keep a house warm at 22°C. How much work is required of the pump to deliver 3100 J of heat into the house if the outdoor temperature is (a) 0°C, (b) \({\bf{ - 15^\circ C}}\)? Assume a COP of 3.0. (c) Redo for both temperatures, assuming an ideal (Carnot) coefficient of performance \({\bf{COP = }}{{\bf{T}}_{\bf{L}}}{\bf{/}}\left( {{{\bf{T}}_{\bf{H}}}{\bf{ - }}{{\bf{T}}_{\bf{L}}}} \right)\).

A Carnot engine operates with\({T_L} = {\bf{20^\circ C}}\)and has an efficiency of 25%. By how many kelvins should the high operating temperature\({T_H}\)be increased to achieve an efficiency of 35%?

Question: (II) A 1.0-L volume of air initially at 3.5 atm of (gauge) pressure is allowed to expand isothermally until the pressure is 1.0 atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.
See all solutions

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