Question

A car tyre is pumped to a pressure of 20000 Nm-2 in the morning when the temperature is 23 oC. Later in the day, the temperature rises to 34 oC. Calculate the new pressure in the tyre. The volume is kept constant.

Answer 1

Answer:

20743.24 Nm¯²

Explanation:

From the question given above, the following data were obtained:

Initial pressure (P1) = 20000 Nm¯²

Initial temperature (T1) = 23 °C

Final temperature (T2) = 34 °C

Final pressure (P2) =?

Volume = constant

Next, we shall convert celsius temperature to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T1) = 23 °C

Initial temperature (T1) = 23 °C + 273 = 296 K

Final temperature (T2) = 34 °C

Final temperature (T2) = 34 °C + 273 = 307 K

Finally, we shall determine the final (i.e the new) pressure of the tyre.

Initial pressure (P1) = 20000 Nm¯²

Initial temperature (T1) = 296 K

Final temperature (T2) = 307 K

Final pressure (P2) =?

Volume = constant

Since the volume is constant, the final (i.e the new) pressure of the tyre can be obtained by using the following formula:

P1/T1 = P2/T2

20000 / 296 = P2 /307

Cross multiply

296 × P2 = 20000 × 307

Divide both side by 296

P2 = (20000 × 307) /296

P2 = 20743.24 Nm¯²

Therefore, the new pressure of the tyre is 20743.24 Nm¯²