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Chapter 19: Q15P (page 578)

Question: Supposeof an ideal gas undergoes an isothermal expansion as energy is added to it as heat Q. If figure shows the final volume Vf versus Q, what is the gas temperature? The scale of the vertical axis is set by Vfs=.30m3, and the scale of the horizontal axis is set by Qs=1200J

Short Answer

Expert verified

Answer

The gas temperature is 360 K

Step by step solution

01

Step 1: Given

The graph Vfvs  Q

Qs=1200Jn=0.825molVf=0.30m3Vi=0.20m3

02

Determine the concept

Using that formula for work done by the gas at a constant temperature and substituting the values from the given graph, find the gas temperature.

Formula is as follow:

W=nRTlnVfVi

Here, W is work done, V is volume, T is temperature, R is universal gas constant and n is number of moles.

03

Determine the gas temperature

For isothermal process,

Q = W

Also,

W=nRTlnVfVi

For isothermal process,

∴Q=nRTlnVfVi∴T=QnRlnVfVi

From the given graph,

Q = 1000 J whenVfs=0.3m2 ,

T=10000.8258.314ln0.300.20T=359.56K≈360K

Hence, the gas temperature is 360 K

Therefore, the temperature of the gas for isothermal process can be found by using the formula for work done by the gas at a constant temperature.

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Most popular questions from this chapter

A gas is to be expanded from initial state i to final state f along either path 1or path 2on a PV diagram. Path1 consists of three steps: an isothermal expansion (work is40 Jin magnitude), an adiabatic expansion (work isin magnitude), and another isothermal expansion (work is20 Jin magnitude). Path2 consists of two steps: a pressure reduction at constant volume and an expansion at constant pressure. What is the change in the internal energy of the gas along path 2?

In a motorcycle engine, a piston is forced down toward the crankshaft when the fuel in the top of the piston’s cylinder undergoes combustion. The mixture of gaseous combustion products then expands adiabatically as the piston descends. Find the average power in (a) watts and (b) horsepower that is involved in this expansion when the engine is running at 4000rpm, assuming that the gauge pressure immediately after combustion is 15atm, the initial volume is 50cm3, and the volume of the mixture at the bottom of the stroke is 250cm3. Assume that the gases are diatomic and that the time involved in the expansion is one-half that of the total cycle.

The dot in Fig 19-18 a represents the initial state of a gas, and the vertical line through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the work W done by the gas is positive, negative, or zero: (a) the gas moves up along the vertical line, (b) it moves down along the vertical line, (c) it moves to anywhere in region 1, and (d) it moves to anywhere in region 2.

In the p-V diagram of Fig.19−17, the gas does5Jof work when taken along isotherm ab and 4Jwhen taken along adiabatic. What is the change in the internal energy of the gas when it is taken along the straight path from a to c?

The temperature of 2.00molof an ideal monoatomic gas is raised 15.0Kat constant volume. What are

  1. The work Wdone by the gas
  2. The energy transferred as heat Q
  3. The changeΔEintin the internal energy of the gas
  4. The changeΔKin average kinetic energy per atom?
See all solutions

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