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A rigid container holds 0.20gof hydrogen gas. How much heat is needed to change the temperature of the gas

a.From50K torole="math" localid="1648534484983" 100K?

b.From localid="1648534491176" 250Kto localid="1648534494324" 300K?

c.From localid="1648534497013" 2250Kto localid="1648534500972" 2300K?

Short Answer

Expert verified

The heat change in temperature of gas from,

a50Kto 100Kis 62J.

b250Kto 300Kis 104J.

cF2250Kto 3000Kis 150J.

Step by step solution

01

Step: 1 a Temperature changes from 50K to 100K:

If the temperature changes by T,then the thermal energy for diatomic gas changes by equation 20.30in the form

ΔEth=nCVΔT

Knowing the mass Mand the molar mass m, we can get the number of moles by

n=Mm=0.2g2g/mol=0.1mol

This thermal energy converts to heat..The temperature change from50Kto 100K. In this range,CV=32R. So, the heat in equation will be

ΔEth=nCVΔT=32nRΔT=32(0.1mol)(8.314J/molK)(100K50K)=62J.

02

Step: 2 b Temperature changes from 250K to 300K:

The temperature changes from 250Kto 300K.In this range,CV=52R.so,the heat equation will be

ΔEth=nCVΔT=52nRΔT=52(0.1mol)(8.314J/molK)(300K250K)=104J.

03

Step: 3 c Temperature changes from 2250K to 3000K:

The temperature changes from 2250Kto 3000K.In this range,CV=72R.so,the heat equation will be

ΔEth=nCVΔT=72nRΔT=72(0.1mol)(8.314J/molK)(2300K2250K)=150J.

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Most popular questions from this chapter

The rms speed of the molecules in 1.0gof hydrogen gas is1800ms .
a. What is the total translational kinetic energy of the gas molecules?
b. What is the thermal energy of the gas?
c. 500Jof work are done to compress the gas while, in the same process, 1200Jof heat energy are transferred from the gas to the environment. Afterward, what in the rms speed of the molecules?

A monatomic gas is adiabatically compressed to 18of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not?

a. The rmsspeed.

b. The mean free path.

c. The thermal energy of the gas.

d. The molar specific heat at constant volume.

Consider a container like that shown in Figure 20.12, with n1moles of a monatomic gas on one side and n2moles of a diatomic gas on the other. The monatomic gas has initial temperature T1i. The diatomic gas has initial temperatureT2i .
a. Show that the equilibrium thermal energies are

E1f=3n13n1+5n2E1i+E2iE2f=5n23n1+5n2E1i+E2i

b. Show that the equilibrium temperature is

Tf=3n1T1i+5n2T2i3n1+5n2

c.2.0g of helium at an initial temperature of role="math" localid="1648474536876" 300Kinteracts thermally with 8.0gof oxygen at an initial temperature of600K . What is the final temperature? How much heat energy is transferred, and in which direction?

A 100cm3box contains helium at a pressure of 2.0atmand a temperature of 100°C. It is placed in thermal contact with a200cm3box containing argon at a pressure of4.0atmand a temperature of 400°C.

a. What is the initial thermal energy of each gas?

b. What is the final thermal energy of each gas?

c. How much heat energy is transferred, and in which direction?

d. What is the final temperature?

e. What is the final pressure in each box?

The number density of an ideal gas at STP is called the Loschmidt number. Calculate the Loschmidt number.

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