TICKET 1-14 1. The compressed air in the cylinder has a temperature of 15^circ C During a fire, the tempera- ture of the air in the cylinder rose to 450^circ C cylinder explode if it is known that at this temperature it can withstand a pressure of no more than 9.8 MP a? The initial pressure of air is 4.8 MPa.

To determine whether the cylinder will explode, we need to use the ideal gas law in the form of the combined gas law, which relates the pressure and temperature of a gas while keeping the volume constant:<br /><br />\[ \frac{P_1}{T_1}frac{P_2}{T_2} \]<br /><br />Where:<br />- \( P_1 \) is the initial pressure<br />- \( T_1 \) is the initial temperature in Kelvin<br />- \( P_2 \) is the final pressure<br />- \( T_2 \) is the final temperature in Kelvin<br /><br />First, convert the temperatures from Celsius to Kelvin:<br />\[ T_1 = 15^{\circ}C + 273.15 = 288.15 \, K \]<br />\[ T_2 = 450^{\circ}C + 273.15 = 723.15 \, K \]<br /><br />Next, use the combined gas law to solve for the final pressure \( P_2 \):<br />\[ P_2 = P_1 \times \frac{T_2}{T_1} \]<br />\[ P_2 = 4.8 \, MPa \times \frac{723.15 \, K}{288.15 \, K} \]<br />\[ P_2 \approx 4.8 \, MPa \times 2.51 \]<br />\[ P_2 \approx 12.05 \, MPa \]<br /><br />Since the final pressure \( P_2 \) (approximately 12.05 MPa) is the maximum pressure the cylinder can withstand (9.8 MPa), the cylinder will not explode.