Question

A storage tank has a volume of 3,000 liters. The tank is originally filled to a pressure of 21.1 megapascals with an ideal gas while the temperature is maintained at 28 degrees Celsius. The tank is heated so the temperature increases to a final temperature of 58 degrees Celsius. What will be the new pressure in the tank in units of megapascals?

Answer 1

It is given that volume is constant i.e 3000 L.

So, $\dfrac{T_1}{P_1}=\dfrac{T_2}{P_2}$

Now,

$T_1=28 +273 = 301\ K\\\\T_2=58 + 273 = 331\ K\\\\P_1 = 21.1\ MPa$

Putting all values in above equation, we get :

$\dfrac{301}{21.1}=\dfrac{331}{P_2}\\\\P_2=\dfrac{331\times 21.1}{301}\ MPa\\\\P_2=23.20\ MPa$

Therefore, the new pressure will be 23.20 MPa.

Hence, this is the required solution.