In an experiment to simulate conditions within an automobile engine, 0.165 mol
of air at a temperature of 720 K
and a pressure of 3.10×106 Pa
is contained in a cylinder of volume 320 cm3
. Then 655 J
of heat is transferred to the cylinder.the volume of the cylinder is allowed to increase while the pressure remains constant, find the final temperature of the air.

To solve this problem, we need to find the final temperature \( T_2 \) of the air after 655 J of heat is added to it under constant pressure. Let's break down the steps to get there.

### Given Data
1. Initial amount of air, \( n = 0.165 \, \text{mol} \)
2. Initial temperature, \( T_1 = 720 \, \text{K} \)
3. Constant pressure, \( P = 3.10 \times 10^6 \, \text{Pa} \)
4. Initial volume, \( V_1 = 320 \, \text{cm}^3 = 3.20 \times 10^{-4} \, \text{m}^3 \)
5. Heat added, \( Q = 655 \, \text{J} \)

### Step 1: Determine the final temperature using the ideal gas law and the heat capacity at constant pressure.
Since the process occurs at constant pressure, we can use the formula relating heat transfer at constant pressure to the change in temperature:

\[
Q = n C_p (T_2 - T_1)
\]

where \( C_p \) is the molar heat capacity at constant pressure for air. For diatomic gases like air, \( C_p \approx 29 \, \text{J/(mol·K)} \).

### Step 2: Substitute values and solve for \( T_2 \).
Rearrange the equation to solve for \( T_2 \):

\[
T_2 = T_1 + \frac{Q}{n C_p}
\]

Substitute the known values:

\[
T_2 = 720 + \frac{655}{0.165 \times 29}
\]

Calculating the term inside the fraction:

\[
T_2 = 720 + \frac{655}{4.785} \approx 720 + 137
\]

\[
T_2 \approx 857 \, \text{K}
\]

### Final Answer
The final temperature \( T_2 \) of the air is approximately **857 K**.

Would you like more details or have any questions?

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Here are 5 related questions to deepen understanding:
1. What assumptions are made about the air to use the ideal gas law here?
2. How would the final temperature change if the pressure were not constant?
3. How would adding more moles of gas initially affect the outcome?
4. What role does the molar heat capacity \( C_p \) play in such problems?
5. Could this process be analyzed using the first law of thermodynamics?

**Tip:** When dealing with gas laws, remember to keep track of units—especially volume, temperature, and pressure.

In an experiment to simulate conditions within an automobile engine, 0.165 mol of air at a temperature of 720 K and a pressure of 3.10×10^6 Pa is contained in a cylinder of volume 320 cm^3. Then 655 J of heat is transferred to the cylinder. The volume of the cylinder is allowed to increase while the pressure remains constant. Find the final temperature of the air.

Learn how to calculate the final temperature of air in an engine cylinder when 655 J of heat is added at a constant pressure of 3.10×10^6 Pa. Using thermodynamic principles and the ideal gas law, this solution walks through each step to reach the final temperature. Ideal for college-level physics students.

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