Question

The volume of an ideal gas is held constant. Determine the ratio P2/P1 of the final pressure to the initial pressure when the temperature of the gas rises (a) from 48 to 96 K and (b) from 26.0 to 68.7 oC.

Answer 1

A. 2

B. 1.14

Step-by-step explanation:

A. Data obtained from the question include:

Initial temperature (T1) = 48K

Final temperature (T2) = 96K

Final pressure (P2)/initial pressure (P1) =?

Since the volume is constant, we shall determine the ratio of final pressure to initial pressure (P2/P1) by applying the following equation:

P1/T1 = P2/T2

P1/48 = P2 /96

Cross multiply

48 x P2 = P1 x 96

Divide both side by 48

P2 = P1 x 96/48

Divide both side P1

P2/P1 = 96/48

P2/P1 = 2

Therefore, the ratio of final pressure to the initial pressure is 2

B. Data obtained from the question include:

Initial temperature (T1) = 26°C = 26°C + 273 = 299K

Final temperature (T2) = 68.7°C = 68.7°C + 273 = 341.7K

Final pressure (P2)/initial pressure (P1) =?

Since the volume is constant, we shall determine the ratio of final pressure to initial pressure (P2/P1) by applying the following equation:

P1/T1 = P2/T2

P1/299 = P2 /341.7

Cross multiply

299 x P2 = P1 x 341.7

Divide both side by 299

P2 = P1 x 341.7/299

Divide both side P1

P2/P1 = 341.7/299

P2/P1 = 1.14

Therefore, the ratio of final pressure to the initial pressure is 1.14