Question

A sample of gas in a rigid steel tank is under 157.9 kPa of pressure at 317 Kelvins.If the tank is heated to 358 Kelvins, what would the new pressure be in kilopascals?178144160210

Answer 1

The new pressure is 178.32kPa.

Given:

A sample of gas in a rigid steel tank is under 157.9 kPa of pressure at 317 Kelvins and the temperature on heating the tank is 58 Kelvins,

To Find:

The new pressure.

Solution:

To find the new pressure we will follow the following steps:

Let the new pressure is P which is in kPa.

As we know,

Temperature is directly proportional to pressure according to Gay Lussa'c law.

Now,

P1/P2 = T1/T2

T2 and T1 are the temperatures of the initial and final states respectively.

Similarly, P2 and P1 are the pressure in initial and final states.

On putting the values we get,

P/157.9 = 358/317

P = (358/317) × 157.9 = 178.32kPa

Henceforth, The new pressure is 178.32kPa.

Answer 2

178kPa

Explanations

According to Gay Lussac's law, the pressure of a given gas is directly proportional to temperature provided that the volume is constant.

`\begin{gathered} P=kT \\ k=(P_1)/(T_1)=(P_2)/(T_2) \end{gathered}`

Given the following parameters

Initial pressure P1 = 157.9kPa

Initial temperature T1 = 317K

Final temperature T2 = 358K

Required

New pressure P2

Substitute

`\begin{gathered} P_2=(P_1T_2)/(T_1) \\ P_2=(157.9*358)/(317) \\ P_2=(56528.2)/(317) \\ P_2\approx178kPa \end{gathered}`

Hence the new pressure in kPa is 178kPa