Q. 29 The volume of a gas is halved du... [FREE SOLUTION]

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) is $1.90 L$ and (b) is $74 掳 C$ .

Step by step solution

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:

$p_{1} V_{2}^{纬} = p_{2} V_{2}^{纬}$

Result on finding the heat ratio g and temperature

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

$p_{1} V_{2}^{纬} = p_{2} V_{2}^{纬}$

On the basis of second volume:

${(\frac{V_{2}}{V_{1}})}^{纬} = p$ ₁p₂鈬�V1V2=p1p2纬

Therefore,

$V_{2} = V_{1} \sqrt[纬]{\frac{p_{1}}{p_{2}}}$

On the basis of ideal gas law and numerically

$V_{2} = \frac{0.1 路 8.314 路 423}{3.101300} \sqrt[1.40]{2} = 1.90 L$

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

$\frac{p_{1} V_{1}}{T_{1}} = \frac{p_{2} V_{2}}{T_{2}}$

Therefore, the temperature is on the basis of numerics:

$T_{2} = \frac{1}{2} \sqrt[1.4]{2} 路 423 = 347 K$

On the basis of Celcius:

$347 K = 347 - 273 = 74 掳 C$

Therefore, the answer for (a) is $1.90 L$ and (b) is $74 掳 C$ .

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91影视

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

Step by step solution

Description

Result on finding the heat ratio g and temperature

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91影视

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

Step by step solution

Description

Result on finding the heat ratio g and temperature

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Force

Physical Quantities And Units

Rotational Dynamics

Fluids

Dynamics

Study anywhere. Anytime. Across all devices.

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?