Answer:
Option A. 327 °C
Step-by-step explanation:
The following data were obtained from the question:
Initial pressure (P1) = 12 atm
Initial temperature (T1) = 27 °C
Final pressure (P2) = 24 atm
Final temperature (T2) =?
Next, we shall convert 27 °C to Kelvin temperature. This can be obtained as follow:
Temperature (K) = Temperature (°C) + 273
Initial temperature (T1) = 27 °C
Initial temperature (T1) = 27 °C + 273
Initial temperature (T1) = 300 K
Next, we shall the temperature at which the cylinder will explode as follow:
Initial pressure (P1) = 12 atm
Initial temperature (T1) = 300 K
Final pressure (P2) = 24 atm
Final temperature (T2) =?
P1/T1 = P2/T2
12/300 = 24/T2
Cross multiply
12 × T2 = 300 × 24
Divide both side by 12
T2 = (300 × 24) /12
T2 = 600 K
Finally, we shall convert 600 K to celsius temperature.
This can be obtained as follow:
Temperature (°C) = Temperature (K) – 273
Temperature (K) = 600 K
Temperature (°C) = 600 – 273
Temperature (°C) = 327 °C
Therefore, the minimum temperature at which the cylinder will explode is
327 °C.