A gas has a volume of 50.0 ml and is heated until it reaches a temperature of 500K and a volume of 0.50 L, What was its original temperature?
The correct answer and explanation is:
To solve for the original temperature, we can use Charles’ Law or the Combined Gas Law, which relates pressure, volume, and temperature of a gas.
The Combined Gas Law is written as: P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
In this problem, we assume pressure is constant, meaning it cancels out. Therefore, the formula simplifies to: V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}
Where:
- V1V_1 = initial volume (50.0 mL = 0.050 L)
- T1T_1 = initial temperature (what we’re solving for)
- V2V_2 = final volume (0.50 L)
- T2T_2 = final temperature (500 K)
Rearranging the equation to solve for T1T_1: T1=V1T2V2T_1 = \frac{V_1 T_2}{V_2}
Substitute the given values: T1=(0.050 L)(500 K)0.50 LT_1 = \frac{(0.050 \, \text{L})(500 \, \text{K})}{0.50 \, \text{L}} T1=250.50=50 KT_1 = \frac{25}{0.50} = 50 \, \text{K}
So, the initial temperature T1T_1 is 50 K.
Explanation:
The relationship between the temperature and volume of a gas is directly proportional when the pressure remains constant. This means that as the temperature increases, the volume increases, and vice versa. By using the Combined Gas Law, we can determine the initial temperature based on the changes in volume and temperature, assuming that the pressure remains constant throughout the process.