Question

Inside the engine of an automobile, the cylinder compresses the air from approximately standard temperature and pressure to one-twentieth of the original volume and a pressure of 50 atm. What is the temperature of the compressed air?

• A. 500 K
• B. 682 K
• C. 550 K
• D. 1000 K
• E. 200 K

Hint:

When all three variables (P, V, T) change, always use the combined gas law directly.

Answer 1

The Correct Option is B

Concept:
For an ideal gas: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

Step 1: Write given data clearly
\[ P_1 = 1 \text{ atm}, \quad T_1 = 273 \text{ K} \] \[ V_2 = \frac{V_1}{20}, \quad P_2 = 50 \text{ atm} \]

Step 2: Substitute in gas equation
\[ \frac{1 \cdot V_1}{273} = \frac{50 \cdot (V_1/20)}{T_2} \]

Step 3: Simplify carefully
\[ \frac{V_1}{273} = \frac{50V_1}{20T_2} \] \[ \frac{1}{273} = \frac{5}{2T_2} \]

Step 4: Solve for temperature
\[ T_2 = \frac{5}{2} \times 273 \] \[ T_2 = 682.5 \approx 682 \text{ K} \] \[ \boxed{682 \text{ K}} \]