To find the new temperature of the gas after the pressure change, you can use the ideal gas law, which states that for a gas at constant volume, the pressure is directly proportional to the temperature in Kelvin. The relationship can be expressed as:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
Where:
- \(P_1\) = Initial pressure
- \(T_1\) = Initial temperature in Kelvin
- \(P_2\) = Final pressure
- \(T_2\) = Final temperature in Kelvin
First, we need to convert the initial temperature from degrees Celsius to Kelvin:
\[ T_1 = 10 , \text{°C} + 273.15 = 283.15 , \text{K} \]
Now substituting the known values into the equation:
- \(P_1 = 700 , \text{mmHg}\)
- \(T_1 = 283.15 , \text{K}\)
- \(P_2 = 900 , \text{mmHg}\)
- \(T_2 = ?\)
Now we can rearrange the formula to solve for \(T_2\):
\[ T_2 = \frac{P_2 \times T_1}{P_1} \]
Substituting the values:
\[ T_2 = \frac{900 , \text{mmHg} \times 283.15 , \text{K}}{700 , \text{mmHg}} \]
Calculating this gives:
\[ T_2 = \frac{900 \times 283.15}{700} \approx \frac{254835}{700} \approx 364.05 , \text{K} \]
Thus, the new temperature \(T_2\) is approximately 364K.
So, the correct answer is (b) 364K.