The pressure in a Red Rider BB gun cartridge is 1.5 atm. If the rifle was at 25 °C prior to firing, what is the temperature change of the cartridge after firing if the cartridge reaches standard air pressure of 1.0 atm?

–99 °C

Explanation:

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

Initial pressure (P₁) = 1.5 atm

Initial temperature (T₁) = 25 °C

Final pressure (P₂) = 1 atm

Change in temperature (ΔT) =?

Next, we shall determine the final temperature. This can be obtained as follow:

Initial pressure (P₁) = 1.5 atm

Initial temperature (T₁) = 25 °C + 273 = 298 K

Final pressure (P₂) = 1 atm

Final temperature (T₂) =?

P₁/T₁ = P₂/T₂

1.5 / 298 = 1 / T₂

Cross multiply

1.5 × T₂ = 298

Divide both side by 1.5

T₂ = 298 / 1.5

T₂ = 199 K

Converting 199 K to °C, we have:

T(°C) = T(K) – 273

T₂ = 199 – 173

T₂ = –74 °C

Finally, we shall determine change in temperature. This can be obtained:

Initial temperature (T₁) = 25 °C

Final temperature (T₂) = –74 °C

Change in temperature (ΔT) =?

ΔT = T₂ – T₁

ΔT = –74 – 25

ΔT = –99 °C

Thus, the change in the temperature is –99 °C

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