Question

a gas is contained in a thick-walled balloon with an initial temperature of 303 k. when the pressure changes from 100.0 kpa to 90.0 kpa, the volume changes from 2.50 l to 3.75 l. what is the final temperature of the system?

Explanation:

Step1: State combined gas law

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

Step2: Rearrange for final temp $T_2$

$$T_2 = \frac{P_2V_2T_1}{P_1V_1}$$

Step3: Substitute given values

$$T_2 = \frac{90.0\ \text{kPa} \times 3.75\ \text{L} \times 303\ \text{K}}{100.0\ \text{kPa} \times 2.50\ \text{L}}$$

Step4: Calculate the result

$$T_2 = \frac{90.0 \times 3.75 \times 303}{100.0 \times 2.50} = 409.05\ \text{K}$$

Answer:

$409\ \text{K}$ (or $409.05\ \text{K}$)