cylinder contain certain volume of gas at 27 degree c.to what temp cylinder subjected so volume increse by 25%
Answers
Explanation:
Given:
Initial Temperature (T1) of the gas = 27° C + 273 ° = 300° K
Let Initial Volume (V1) of the gas be "V".
We have to find:
The temperature (T2) when, volume of the gas (a) increases by 25% and (b) decreases by 25%.
From (a).
Final Volume (V2) of the gas = V * (100 + 25) / 100
→ V2 = V * 125/100
→ V2 = 5V/4
We know that,
Charlie's law of gases states that at constant pressure the Volume. of a gas is directly proportional to it's temperature.
\sf \implies \: \large{ v \: \: \propto \: \: t}⟹v∝t
→ V/T = K
→ V1 / T1 = V2 / T2
→ V/300 = (5V/4) / T2
On cross multiplication we get,
→ T2* V = 300 * 5V/4
→ T2 * V = 375V
→ T2 = 375V/V
→ T2 = 375° K
→ T2 = 375° - 273°
→ T2 = 102° C
From (b).
Final Volume = V * (100 - 25)/100
→ V2 = V*75/100
→ V2 = 3V/4
Using the same formula,
→ V / 300 = (3V/4) / T2
→ T2 * V = 300 * 3V/4
→ T2 * V = 225V
→ T2 = 225V/V
→ T2 = 225° K
→ T2 = 225 - 273
→ T2 = - 48° C
Hence, the Temperature is
Increased to 102° C when the Volume is increased by 25%.
Decreased to - 48° C when the Volume is decreased by 25%.