Question

A gas is placed in a storage tank at a pressure of 49.2 atm at 39.0C . As a safety device, a small metal plug in the tank is made of a metal alloy that melts at 198C . If the tank is heated, what is the maximum pressure that will be attained in the tank before the plug melts and releases gas?

Answer 1

The maximum pressure that will be attained in the tank before the plug melts and releases gas should be less than 74.26 atm.

Step-by-step explanation:

To calculate the final pressure of the system, we use the equation given by Gay-Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

`(P_1)/(T_1)=(P_2)/(T_2)`

where,

`P_1\text{ and }T_1` are the initial pressure and temperature of the gas.

`P_2\text{ and }T_2` are the final pressure and temperature of the gas.

We are given:

`P_1=49.2 atm\\T_1=39.0^oC = 312.15 K\\P_2=?\\T_2=198^oC=471.15 K`

Putting values in above equation, we get:

`(49.2atm )/(312.15 K)=(P_2)/(471.15 K)\\\\P_2=74.26 atm`

The maximum pressure that will be attained in the tank before the plug melts and releases gas should be less than 74.26 atm.