What is the temperature increase of the gas?

In summary, the conversation discusses the effect of pumping air into an empty rubber raft, and how it affects the pressure and temperature of the air. The work done on the gas is calculated to be 0.32 J, and using the ideal gas law and assuming the initial temperature of the air to be 293 K, the temperature increase of the gas is found to be 0.00046 K. Additional attempted solutions using equations such as Q = ΔU and ΔU = nCvΔT are also mentioned.
  • #1
Tori Grafe
1
0

Homework Statement


In an empty rubber raft the pressure is approximately constant. You push on a large air pump that pushes 1.0L (1.0×10^−3 m^3) of air into the raft. You exert a 16N force while pushing the pump handle 2.0×10^−2 m .

Part A: Determine the work done on the gas.
Part B: If all of the work is converted to thermal energy of the 1.0 L of gas, what is the temperature increase of the gas? Assume that the air obeys the ideal gas law and is initially at 293 K.

2. Homework Equations

Just trying to come up with some equations that may help, although I have had no luck...
P*V=n*R*T
Work = -n*R*deltaT
W= (-/+) deltaP*V
Delta T = Q/c*m
Uthermal = 3/2*n*R*T
delta U = c*m*delta T

The Attempt at a Solution


Part A: I have already solved this part as you can see below...
Work = Force * Distance
Work = 16 N * 2.0x10^-2 m
Work = .32 N*m
Work = .32 (kg*m^2)/s^2
Work = .32 J

Part B: I have attempted a couple of times as you can see below... I really need help on this
Work = Q
Delta T = Q/c*m
m = ro * v
ro = 1.3 kg/m^3
v= 1.0x10^-3 m^3
c= 700 J/(kg * degrees C)
m = 1.3x10^-3 kg

delta T = .32J / (700 (J/(kg * degrees C)) * 1.3x10^-3 kg)

Work = -delta P * v
.32 J = -delta P * 1.0x10^-3
-delta P = 320 N/m^2
320 N/m^2 = n*R*delta T
320 N/m^2 = n*(8.314 J/mol * K)*delta T
 
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  • #2
I think the equation
ΔU=nCvΔT
Might help you.
 

1. What is the definition of temperature increase?

Temperature increase refers to the change in temperature of a substance or gas over a period of time. It is typically measured in degrees Celsius or Fahrenheit and can be positive or negative.

2. How is the temperature increase of a gas calculated?

The temperature increase of a gas can be calculated using the equation: ΔT = (Tf - Ti), where ΔT is the change in temperature, Tf is the final temperature, and Ti is the initial temperature.

3. What factors can cause an increase in gas temperature?

There are several factors that can cause an increase in gas temperature, including the addition of heat, compression, chemical reactions, and changes in pressure or volume.

4. What is the significance of measuring temperature increase in gases?

Measuring temperature increase in gases is important for understanding the behavior of gases and how they interact with their surroundings. It is also crucial in many scientific fields such as thermodynamics, chemistry, and atmospheric science.

5. How does the temperature increase of a gas relate to the kinetic theory of gases?

The kinetic theory of gases states that the temperature of a gas is directly proportional to the average kinetic energy of its particles. Therefore, an increase in temperature results in an increase in the kinetic energy of gas particles, leading to a higher gas temperature.

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