isoprocesses

1. What are isoprocesses?

Solution:

Isoprocesses are processes in an ideal gas with constant mass, during which one of the state variables remains constant.

A) Isothermal process (T = constant)
Boyle–Mariotte’s law

p1V1=p2V2,ΔU=0⇒Q=−W=W′p_1 V_1 = p_2 V_2, \quad \Delta U = 0 \quad \Rightarrow \quad Q = -W = W'

The heat received by an ideal gas during an isothermal process is used to perform work.

B) Isochoric process (V = constant)
Charles’s law

p1T1=p2T2,W=0⇒ΔU=Q=ncvΔT\frac{p_1}{T_1} = \frac{p_2}{T_2}, \quad W = 0 \quad \Rightarrow \quad \Delta U = Q = n c_v \Delta T

The heat received by an ideal gas in an isochoric process is used to increase its internal energy.

C) Isobaric process (p = constant)
Gay–Lussac’s law

V1T1=V2T2,ΔU=W+ncpΔT\frac{V_1}{T_1} = \frac{V_2}{T_2}, \quad \Delta U = W + n c_p \Delta T

The heat received by an ideal gas during an isobaric process is used both to change internal energy and to perform work.

D) Adiabatic process (Q = 0) – no heat exchange occurs between the gas and the surroundings. p,V,Tp, V, T may change.

Poisson’s law

p1V1κ=p2V2κp_1 V_1^\kappa = p_2 V_2^\kappa T1V1κ−1=T2V2κ−1,ΔU=W=−W′T_1 V_1^{\kappa-1} = T_2 V_2^{\kappa-1}, \quad \Delta U = W = -W' κ=cpcv>1Poisson’s constant for the gas\kappa = \frac{c_p}{c_v} > 1 \quad \text{Poisson’s constant for the gas

  • cpc_p – specific heat capacity at constant pressure

  • cvc_v – specific heat capacity at constant volume


 

2.What volume will 30 liters of air have if, at the same temperature, we increase its pressure from 72 kPa to 75 kPa?

Solution:

Analysis:

V1 = 30 l = 30·10-3 m3,  p1 = 72·103 Pa,  p2 = 75·103 Pa, V2 = ?

 fyzika-izodeje-2.gif

After increasing the pressure the air will have a volume of 28.8 liters.

3.The density of helium at pressure 105 Pa is ρ1 = 0.164 kg·m-3. What will its density be if we compress it to a pressure of 5·107 Pa? (The mass and temperature of the gas do not change during compression).

Solution:

Analysis:

p1 = 105 Pa,   ρ1 = 0.164 kg·m-3 ,  p2 = 5·107 Pa,  ρ2 = ?

fyzika-izodeje-3.gif 

The density of helium after compression will be 82 kg·m-3.

4.The density of air under normal conditions is ρ1 = 1.3 kg·m-3. What will the density of the air be if we heat it from normal conditions to 30oC? (The amount of air does not change).

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5.A gas enclosed in a container with a movable piston is heated at constant pressure from 22oC to 52oC. By what percentage did its volume increase?

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6. A bulb is filled with nitrogen during manufacturing at a pressure of 50.6 kPa and a temperature of 18oC. What is the temperature of the nitrogen in the lit bulb if its pressure increases to 118 kPa?

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7.At a Formula 1 race, the temperature of the air in the tires increased from 19oC to 79oC. How does the pressure in the tire change if it was originally inflated to 240 kPa? Why is a "formation lap" performed before the start? (The internal volume of the tire does not change)

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8.In a cylindrical chamber there is air closed by a movable piston located 50 cm from the bottom of the cylinder. The air pressure is 105 Pa. If the piston is moved 20 cm toward the bottom during adiabatic compression, the air pressure increases to 2.05·105 Pa. Determine the Poisson constant for air!

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9.Show that for an adiabatic process T1·V1κ-1 = T2·V2κ-1

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10. For adiabatic compression the volume of the air was reduced to 1/10 of the original volume. Calculate the pressure and temperature of the air after adiabatic compression. The initial air pressure was 105 Pa, the initial temperature 20oC. κ (air) = 1.4

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11.The pressure of a gas in a closed container at a temperature of 110C is 189 kPa. What will be the temperature of this gas if its pressure increases to 1 MPa?

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12.The pressure of a gas at a temperature of 200C is 107 kPa. What will its pressure be if its temperature increases to 1500C?

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13.The temperature of oxygen with a given mass increases isobarically from an initial temperature of -200C. At what temperature does the oxygen have 1.5 times the volume it had at the initial temperature?

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14.What process is written in the table:

izodeje-14z
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15.The volume of a gas is 25 liters with a pressure of 1 kPa. What will its pressure be if we reduce its volume to 20% of the original volume?

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16.A cylindrical container 30 cm long is closed with a movable piston. A gas in the container is under a pressure of 0.5 MPa. Determine its pressure if the internal volume of the container increases by moving the piston by 10 cm.

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17.The mean free path of a molecule   izodeje-17z  is at pressure p1 = 105Pa. What will the mean free path of the molecule be at a pressure of

  • a.) 1.0 Pa,
  • b.) 107Pa.
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18.Hydrogen H2 has a temperature of -30C. By adiabatic expansion its volume increases to three times the original volume. What is the resulting temperature of the hydrogen during this adiabatic process?

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19.Argon has, at normal pressure p1 = 101325 Pa, a volume V1 = 10 liters. After adiabatic compression its volume changes to V2 = 4 liters and the pressure to p2 = 0.468 MPa. Determine the Poisson constant for argon.

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20.Determine the specific heat capacity of argon at constant volume cV, if the specific heat capacity of argon at constant pressure is

cP = 525 J.kg-1.K-1.
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