Question

At 400 K, an ideal gas is enclosed in a 0.5 m\(^3\) vessel at a pressure of 203 kPa. What is the change in temperature required (in K), if it occupies a volume of 0.2 m\(^3\) under a pressure of 304 kPa? (Nearest integer)

• A. 240
• B. 160
• C. 120
• D. 80
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Hint:

Use the combined gas law: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] to find the unknown temperature when pressure and volume change.

Answer 1

The Correct Option is B

Step 1: Applying the General Gas Law
For an ideal gas: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] where:
- \( P_1 = 203 \) kPa, \( V_1 = 0.5 \) m\(^3\), \( T_1 = 400 \) K
- \( P_2 = 304 \) kPa, \( V_2 = 0.2 \) m\(^3\), \( T_2 = ? \) Step 2: Rearranging the Equation \[ T_2 = \frac{P_2 V_2 T_1}{P_1 V_1} \] Step 3: Substituting Values \[ T_2 = \frac{(304)(0.2)(400)}{(203)(0.5)} \] \[ T_2 = \frac{24320}{101.5} \approx 160 K \] Thus, the temperature change required is \( 160 \) K. \bigskip