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Chapter 19: Q. 29 (page 544)

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5.

a. What is the specific heat ratio g?

b. By what factor does the temperature increase?

Short Answer

Expert verified

The answer for (a) is1.90Land (b) is74°C.

Step by step solution

01

Description 

As per provided information, the volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5.

On the basis of adiabatic process, it can be written as:

p1V2γ=p2V2γ

02

Result on finding the heat ratio g and temperature 

On the basis of adiabatic process, it can be written as:

p1V2γ=p2V2γ

On the basis of second volume:

(V2V1)γ=p1p2⇒V1V2=p1p2γ

Therefore,

V2=V1p1p2γ

On the basis of ideal gas law and numerically

V2=0.1·8.314·4233.10130021.40=1.90L

Thus, as per the ideal gas law when mole number is constant:

p1V1T1=p2V2T2

Therefore, the temperature is on the basis of numerics:

T2=1221.4·423=347K

On the basis of Celcius:

347K=347-273=74°C

Therefore, the answer for (a) is 1.90Land (b) is 74°C.

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Most popular questions from this chapter

Why is the molar specific heat of a gas at constant pressure larger than the molar specific heat at constant volume?

The gas cylinder in Figure Q19.11 is well insulated on all sides. The piston can slide without friction. Many small masses on top of the piston are removed one by one until the total mass is reduced by 50%.

a. During this process, are (i) ∆T, (ii) W, and (iii) Q greater than, less than, or equal to zero? Explain.

b. Draw a pV diagram showing the process.

A 500 g metal sphere is heated to 300C, then dropped into a

beaker containing 300 cm3 of mercury at 20.0C. A short time later

the mercury temperature stabilizes at 99.0C. Identify the metal.

You come into the lab one day and find a well-insulated 2000mL thermos bottle containing 500mL of boiling liquid nitrogen. The remainder of the thermos has nitrogen gas at a pressure of 1.0 atm. The gas and liquid are in thermal equilibrium. While waiting for lab to start, you notice a piece of iron on the table with " 197g" written on it. Just for fun, you drop the iron into the thermos and seal the cap tightly so that no gas can escape. After a few seconds have passed, what is the pressure inside the thermos? The density of liquid nitrogen is 810kg/m3.

The gas cylinder in Figure Q19.9 is a rigid container that is well insulated except for the bottom surface, which is in contact with a block of ice. The initial gas temperature is 7 0°C.

a. During the process that occurs until the gas reaches a new equilibrium, are (i) ∆T, (ii) W, and (iii) Q greater than, less than, or equal to zero? Explain.

b. Draw a pV diagram showing the process
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