Question 1

The fact that most solids have molar heat capacities of approximately 3R,where R is the universal gas constant,is known as

Accepted Answer

The Dulong-Petit law states that most solids have molar heat capacities of approximately 3R. This law was discovered empirically in the early 19th century and is named after its discoverers, Pierre Louis Dulong and Alexis Thérèse Petit. The equipartition theorem and Joule's principle are related to different aspects of thermodynamics, but they do not specifically explain the molar heat capacities of solids. The first law of thermodynamics is a fundamental principle that relates to the conservation of energy, but it is not directly related to the molar heat capacities of solids.

Question 2

The pressure of a mass of air at 20S1U1P1$\circ$S1S1P0C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting temperature.

Accepted Answer

Using the adiabatic process formula $ T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{(\gamma-1)/\gamma} $, where $ \gamma = 1.41 $, $ T_1 = 20°C $, and $ P_2/P_1 = 0.5 $, the resulting temperature $ T_2 $ is approximately -33.0°C.

Question 3

At a particular point on a PV diagram,the magnitude of the slope of a curve that represents an adiabatic process is

Accepted Answer

The slope of an adiabatic process curve represents the ratio of change in pressure to change in volume, which is given by -γPV, where γ is the ratio of specific heats for the gas. The magnitude of γ is greater than 1, which means that the slope of the adiabatic process curve is steeper than that of an isotherm, where γ = 1. Therefore, the answer is E, which means that the slope of the adiabatic process curve is greater than that of an isotherm through the same point.

Question 4

An ideal monatomic gas has a molar heat capacity C_mp at constant pressure.What is the molar heat capacity at constant volume of an ideal diatomic gas?

Accepted Answer

The answer of An ideal monatomic gas has a molar...

Question 5

The pressure of a mass of air at 20S1U1P1$\circ$S1S1P0C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting volume.

Accepted Answer

According to the adiabatic process of an ideal gas, we have
P1V1^γ = P2V2^γ
where γ = CP/CV = 1.41 is the ratio of specific heats of air.
Since the pressure is halved, P2 = P1/2.
Solving the above equation for V2, we get
V2 = V1(P1/P2)^(1/γ) = 1.63*V1
Therefore, the resulting volume is 1.63 times the original volume.
Hence, the correct answer is B.

Question 6

"The specific heat of an ideal gas at constant pressure C_p is greater than the specific heat of a gas at constant volume C_v." Which of the following describes this statement?

Accepted Answer

The statement is true because when heating an ideal gas at constant pressure, the gas expands doing work on the surroundings, which requires more heat energy input to raise the temperature of the gas. In contrast, when heating an ideal gas at constant volume, no work is done by the gas, and thus less heat energy is required to increase the temperature, resulting in a lower specific heat. Therefore, the statement is supported by the fact that at constant pressure, more work is done and therefore more heat energy is needed to raise the temperature of the gas.

Question 7

In a system composed of an ideal gas contained in a cylinder fitted with a piston,a reversible adiabatic expansion causes the temperature of the gas to drop because

Accepted Answer

In a reversible adiabatic process, no heat is exchanged with the surroundings. The work done by the gas during expansion comes from its internal energy, leading to a decrease in temperature.

Question 8

The internal energy of a solid depends on the number of degrees of freedom available to each atom.Which of the following statements is correct concerning these degrees of freedom in a solid?

Accepted Answer

In a solid, the atoms are not free to move around or rotate as they would in gases or liquids. Instead, their movement is restricted to vibrations about their fixed positions. Each atom in a solid has three degrees of freedom associated with kinetic energy (due to the vibrations in three perpendicular directions) and three corresponding degrees of freedom associated with potential energy (also due to vibrations in those directions), making a total of six degrees of freedom related to vibrational motion.

Question 9

When a gas is compressed adiabatically,

Accepted Answer

When a gas is compressed adiabatically, work is done on the system, causing the temperature of the gas to rise. This is because the energy input from the work done increases the internal energy of the gas, which is manifested as an increase in temperature.

Question 10

A cylinder contains 20 L of air at 1 atm.The ratio of C_p to C_V for air is 1.41.If this sample of air is compressed adiabatically to a volume of 5 L,the pressure after compression is approximately

Accepted Answer

For adiabatic processes, $ P_1 V_1^\gamma = P_2 V_2^\gamma $. Given $ \gamma = 1.41 $, $ P_1 = 1 $ atm, $ V_1 = 20 $ L, and $ V_2 = 5 $ L, solve for $ P_2 $: $ P_2 = P_1 \times (V_1/V_2)^\gamma = 1 \times (20/5)^{1.41} \approx 7.1 $ atm.

Question 11

A gas can absorb heat without changing temperature if at the same time

Accepted Answer

A gas can absorb heat without changing temperature if it does sufficient work in expanding, as the energy absorbed as heat is used to do work, maintaining the internal energy and thus the temperature constant.

Question 12

A gas has a molar heat capacity at constant volume of 28.39 J/mol · K.Assume the equipartition theorem to be valid.How many degrees of freedom (including translational)are there for the molecules of this gas? (the ideal-gas law constant is R = 8.31 J/mol · K)

Accepted Answer

The molar heat capacity at constant volume (Cv) is given by Cv = (f/2)R, where f is the degrees of freedom. Solving for f: 28.39 J/mol·K = (f/2)(8.31 J/mol·K), f = 7.

Question 13

Calculate the speed of sound in hydrogen gas (H₂)at 20S1U1P1$\circ$S1S1P0C given the ratio of C_p to C_v is 1.41.(Molar mass of H₂= 2 g/mol.)

Accepted Answer

The answer of Calculate the speed of sound in hydrogen...

Question 14

In an adiabatic reversible compression of an ideal gas,there is a decrease in

Accepted Answer

In an adiabatic reversible compression of an ideal gas, the volume decreases as the gas is compressed. The pressure and temperature increase due to the work done on the gas, which also increases its internal energy. The rms molecular velocity increases as a result of the increased temperature.

Question 15

An ideal gas with an initial volume of 3 L at a pressure of 2 atm is compressed adiabatically until it has a volume of 2 L; then it is cooled at constant volume until its temperature drops to its initial value.The final pressure is

Accepted Answer

The answer of An ideal gas with an initial volume...

Question 16

The molar heat capacity at constant volume of a gas is found to be 20.74 J/mol · K.What is the molar heat capacity at constant pressure of this gas? (The ideal-gas law constant is R = 8.31 J/mol · K)

Accepted Answer

The relationship between molar heat capacity at constant pressure (Cp) and molar heat capacity at constant volume (Cv) for an ideal gas is:

Cp - Cv = R

where R is the ideal-gas law constant.

Rearranging this equation, we can solve for Cp:

Cp = Cv + R

Plugging in the given value of Cv (20.74 J/mol · K) and R (8.31 J/mol · K), we get:

Cp = 20.74 J/mol · K + 8.31 J/mol · K = 29.05 J/mol · K

Therefore, the molar heat capacity at constant pressure of this gas is approximately 29.0 J/mol · K, which is closest to choice B.

Question 17

The equipartition theorem

Accepted Answer

The equipartition theorem fails to explain the fact that monatomic atoms do not rotate about any of three possible mutually perpendicular axes, is unable to account for the dependency of heat capacities on temperature, fails to predict correctly the heat capacities of solids at high temperatures, and does not acknowledge the quantization of energy. Therefore, all of these statements are correct, making E the best choice.

Question 18

In a system composed of gas contained in a cylinder fitted with a piston,an adiabatic expansion causes the temperature of the gas to drop because

Accepted Answer

An adiabatic process is one in which no heat is exchanged between the system and the surroundings. Therefore, the drop in temperature of the gas must be due to the work done by the system. In an adiabatic expansion, the gas performs work on the piston, and as a result, the internal energy of the gas decreases. This work is done entirely at the expense of the internal energy of the gas, hence the correct choice is D.

Question 19

The difference in the molar heat capacity at constant P and constant V is (assume ideal gas).

Accepted Answer

The difference in the molar heat capacity at constant pressure (Cp) and constant volume (Cv) for an ideal gas is equal to the gas constant R, regardless of the type of gas (monatomic, diatomic, or polyatomic). This is a result of the ideal gas law and the definition of heat capacities.

Question 20

A system is said to go through an adiabatic process if,throughout the process,

Accepted Answer

Adiabatic process means no exchange of heat between the system and surroundings. Hence, the correct option is C. Option A refers to an isothermal process, Option B refers to an isochoric process, Option D contradicts the concept of energy conservation, and Option E refers to an isobaric process.

Quiz 18: Heat and the First Law of Thermodynamics

The fact that most solids have molar heat capacities of approximately 3R,where R is the universal gas constant,is known as

The pressure of a mass of air at 20^$\circ$C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting temperature.

At a particular point on a PV diagram,the magnitude of the slope of a curve that represents an adiabatic process is

An ideal monatomic gas has a molar heat capacity C_mp at constant pressure.What is the molar heat capacity at constant volume of an ideal diatomic gas?

The pressure of a mass of air at 20^$\circ$C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting volume.

"The specific heat of an ideal gas at constant pressure C_p is greater than the specific heat of a gas at constant volume C_v." Which of the following describes this statement?

In a system composed of an ideal gas contained in a cylinder fitted with a piston,a reversible adiabatic expansion causes the temperature of the gas to drop because

The internal energy of a solid depends on the number of degrees of freedom available to each atom.Which of the following statements is correct concerning these degrees of freedom in a solid?

When a gas is compressed adiabatically,

A cylinder contains 20 L of air at 1 atm.The ratio of C_p to C_V for air is 1.41.If this sample of air is compressed adiabatically to a volume of 5 L,the pressure after compression is approximately

A gas can absorb heat without changing temperature if at the same time

A gas has a molar heat capacity at constant volume of 28.39 J/mol · K.Assume the equipartition theorem to be valid.How many degrees of freedom (including translational) are there for the molecules of this gas? (the ideal-gas law constant is R = 8.31 J/mol · K)

Calculate the speed of sound in hydrogen gas (H₂) at 20^$\circ$C given the ratio of C_p to C_v is 1.41.(Molar mass of H₂= 2 g/mol.)

In an adiabatic reversible compression of an ideal gas,there is a decrease in

An ideal gas with an initial volume of 3 L at a pressure of 2 atm is compressed adiabatically until it has a volume of 2 L; then it is cooled at constant volume until its temperature drops to its initial value.The final pressure is

The molar heat capacity at constant volume of a gas is found to be 20.74 J/mol · K.What is the molar heat capacity at constant pressure of this gas? (The ideal-gas law constant is R = 8.31 J/mol · K)

The equipartition theorem

In a system composed of gas contained in a cylinder fitted with a piston,an adiabatic expansion causes the temperature of the gas to drop because

The difference in the molar heat capacity at constant P and constant V is (assume ideal gas) .

A system is said to go through an adiabatic process if,throughout the process,

Quiz 18: Heat and the First Law of Thermodynamics

The fact that most solids have molar heat capacities of approximately 3R,where R is the universal gas constant,is known as

The pressure of a mass of air at 20 ∘\circ∘ C is halved adiabatically.If the ratio of Cp to Cv for air is 1.41,calculate the resulting temperature.

At a particular point on a PV diagram,the magnitude of the slope of a curve that represents an adiabatic process is

An ideal monatomic gas has a molar heat capacity Cmp at constant pressure.What is the molar heat capacity at constant volume of an ideal diatomic gas?

The pressure of a mass of air at 20 ∘\circ∘ C is halved adiabatically.If the ratio of Cp to Cv for air is 1.41,calculate the resulting volume.

"The specific heat of an ideal gas at constant pressure Cp is greater than the specific heat of a gas at constant volume Cv." Which of the following describes this statement?

In a system composed of an ideal gas contained in a cylinder fitted with a piston,a reversible adiabatic expansion causes the temperature of the gas to drop because

The internal energy of a solid depends on the number of degrees of freedom available to each atom.Which of the following statements is correct concerning these degrees of freedom in a solid?

When a gas is compressed adiabatically,

A cylinder contains 20 L of air at 1 atm.The ratio of Cp to CV for air is 1.41.If this sample of air is compressed adiabatically to a volume of 5 L,the pressure after compression is approximately

A gas can absorb heat without changing temperature if at the same time

A gas has a molar heat capacity at constant volume of 28.39 J/mol · K.Assume the equipartition theorem to be valid.How many degrees of freedom (including translational) are there for the molecules of this gas? (the ideal-gas law constant is R = 8.31 J/mol · K)

Calculate the speed of sound in hydrogen gas (H2) at 20 ∘\circ∘ C given the ratio of Cp to Cv is 1.41.(Molar mass of H2 = 2 g/mol.)

In an adiabatic reversible compression of an ideal gas,there is a decrease in

An ideal gas with an initial volume of 3 L at a pressure of 2 atm is compressed adiabatically until it has a volume of 2 L; then it is cooled at constant volume until its temperature drops to its initial value.The final pressure is

The molar heat capacity at constant volume of a gas is found to be 20.74 J/mol · K.What is the molar heat capacity at constant pressure of this gas? (The ideal-gas law constant is R = 8.31 J/mol · K)

The equipartition theorem

In a system composed of gas contained in a cylinder fitted with a piston,an adiabatic expansion causes the temperature of the gas to drop because

The difference in the molar heat capacity at constant P and constant V is (assume ideal gas) .

A system is said to go through an adiabatic process if,throughout the process,

The pressure of a mass of air at 20^$\circ$C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting temperature.

An ideal monatomic gas has a molar heat capacity C_mp at constant pressure.What is the molar heat capacity at constant volume of an ideal diatomic gas?

The pressure of a mass of air at 20^$\circ$C is halved adiabatically.If the ratio of C_p to C_v for air is 1.41,calculate the resulting volume.

"The specific heat of an ideal gas at constant pressure C_p is greater than the specific heat of a gas at constant volume C_v." Which of the following describes this statement?

A cylinder contains 20 L of air at 1 atm.The ratio of C_p to C_V for air is 1.41.If this sample of air is compressed adiabatically to a volume of 5 L,the pressure after compression is approximately

Calculate the speed of sound in hydrogen gas (H₂) at 20^$\circ$C given the ratio of C_p to C_v is 1.41.(Molar mass of H₂= 2 g/mol.)